From 1997 to 2001 I was working on a project devoted to the numerical solution of boundary value problems for ordinary differential equations. This project was funded by the Austrian Science Fund under grant no. P-12507 MAT. The project was continued from 2002 to 2003 under grant no. P-15072 MAT. Comprehensive documentation of the activities can be found on our project homepage. From 2003 to 2004, I was working as a group leader in the Special Research Program (SFB) AURORA of the Austrian Science Fund, and from 2004 to 2005 with the SFB 382 at the Eberhard Karls University in Tübingen. Then, from 2005 to 2006, I was employed with the Institute of Materials Chemistry at Vienna University of Technology. From 2007 to 2010, I was funded by the APART scholarship of the Austrian Academy of Sciences. From 2010 to 2011, I was employed with the Austrian Science Fund's project P21742-N16 at the University of Vienna. From 2011 to 2014, I was assistant professor at Vienna University of Technology. From 2015 to 2018, I was employed with my research project MA14-002 funded by the Vienna Science and Technology Fund at the University of Vienna. Since 2018, I am employed with my research project P 30819-N32 funded by the Austrian Science Fund. So far, my research yielded the following refereed papers, other publications and talks :

• O. Koch, Numerische Lösung singulärer Anfangswertprobleme zweiter Ordnung, Thesis, Vienna University of Technology, Austria, 1998.
  
  You can view the abstract of my thesis or download the entire text as a .pdf file.
  
  Refereed Papers
  
  
• O. Koch, P. Kofler, E. B. Weinmüller, The Implicit Euler Method for the Numerical Solution of Singular Initial Value Problems, Appl. Numer. Math. 34(2000), pp. 231-252.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, P. Kofler, E. B. Weinmüller, Initial Value Problems for Systems of Ordinary First and Second Order Differential Equations with a Singularity of the First Kind, Analysis 21(2001), pp. 373-389.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, E. B. Weinmüller, Iterated Defect Correction for the Solution of Singular Initial Value Problems, SIAM J. Numer. Anal. 38(2001), pp. 1784-1799.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, E. B. Weinmüller, Theory and Solution Techniques for Singular Boundary Value Problems for Ordinary Differential Equations, in: Parallel Processing and Applied Mathematics (M.P.R. Wyrzykowski, J. Dongarra, and J. Wasniewsky, eds.), Springer Lecture Notes in Computer Science 2328(2002), pp. 851-861.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, E. B. Weinmüller, The Convergence of Shooting Methods for Singular Boundary Value Problems, Math. Comp. 72(2003), pp. 289-305.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, E. B. Weinmüller, Efficient Collocation Schemes for Singular Boundary Value Problems, Numer. Algorithms 31(2002), pp. 5-25.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, G. Kneisl, O. Koch, E. B. Weinmüller, A Collocation Code for Boundary Value Problems in Ordinary Differential Equations, Numer. Algorithms 33(2003), pp. 27-39.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, E. B. Weinmüller, Analytical and Numerical Treatment of a Singular Initial Value Problem in Avalanche Modeling, Appl. Math. Comput. 148(2004), pp. 561-570.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, E. B. Weinmüller, New Variants of Defect Correction for Boundary Value Problems in Ordinary Differential Equations, in Current Trends in Scientific Computing, Z. Chen, R. Glowinski, K. Li (eds), Contemp. Math. 329(2003), pp. 43-50.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, E. B. Weinmüller, Collocation Methods for Boundary Value Problems with an Essential Singularity, in: Large-Scale Scientific Computing (I. Lirkov, S. Margenov, J. Wasniewski, and P. Yalamov, eds.), Springer Lecture Notes in Computer Science 2907, pp. 347-354.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, Discrete Event Simulation of the Transport Logistics of the Austrian Red Cross, SNE Simulation News Europe, 38/39(2003), pp. 10-15.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, E. B. Weinmüller, Analysis of a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problems, SIAM J. Numer. Anal. 42(2005), pp. 2366-2386.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, H. Weigl, Modeling Ambulance Service of the Austrian Red Cross, Proceedings of the Winter Simulation Conference 2003, pp. 701-706.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, D. Praetorius, E. B. Weinmüller, New a Posteriori Error Estimates for Singular Boundary Value Problems, Numer. Algorithms 40(2005), pp. 79-100.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, Asymptotically Correct Error Estimation for Collocation Methods Applied to Singular Boundary Value Problems, Numer. Math. 101(2005), pp. 143-164.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• C.J. Budd, O. Koch, E. B. Weinmüller, Computation of Self-Similar Solution Profiles for the Nonlinear Schrödinger Equation, Computing 77(2006), pp. 335-346.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• J. Caillat, J. Zanghellini, M. Kitzler, W. Kreuzer, O. Koch, A. Scrinzi, Correlated Multielectron Systems in Strong Laser Pulses - An MCTDHF Approach, Phys. Rev. A 71(2005), pp. 012712.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• C.J. Budd, O. Koch, E. B. Weinmüller, From Nonlinear PDEs to Singular ODEs, Appl. Numer. Math. 56(2006), pp. 413-422.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, E. B. Weinmüller, Efficient Mesh Selection for Collocation Methods Applied to Singular BVPs, J. Comput. Appl. Math. 180(2005), pp. 213-227.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• H. Hofstätter, O. Koch, Analysis of a Defect Correction Method for Geometric Integrators, Numer. Algorithms 41(2006), pp. 103-126.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, W. Kreuzer, A. Scrinzi, Approximation of the Time-Dependent Electronic Schrödinger Equation by MCTDHF, Appl. Math. Comput. 173(2006), pp. 960-976.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• G. Kitzhofer, O. Koch, P. Lima, E. B. Weinmüller, Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics, J. Sci. Comput. 32(2007), pp. 411-424.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, C. Lubich, Regularity of the Multi-Configuration Time-Dependent Hartree Approximation in Quantum Molecular Dynamics, M2AN Math. Model. Numer. Anal. 41(2007), pp. 315-331.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, C. Lubich, Dynamical Low Rank Approximation, SIAM J. Matrix Anal. Appl. 29(2007), pp. 434-454.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• G. Kitzhofer, O. Koch, E. B. Weinmüller, Pathfollowing for Essentially Singular Boundary Value Problems with Application to the Complex Ginzburg-Landau Equation, BIT 49(2009), pp. 141-160.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, Efficient Computation of the MCTDHF Approximation to the Time-Dependent Schrödinger Equation, Opuscula Math. 26(2006), pp. 473-487.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, E. Karner, O. Koch, E. B. Weinmüller, Collocation Methods for the Solution of Eigenvalue Problems for Singular Ordinary Differential Equations, Opuscula Math. 26(2006), pp. 29-41.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, R. März, D. Praetorius, E. B. Weinmüller, Collocation Methods for Index-1 DAES with a Critical Point, Oberwolfach Report No. 18, ID 06016(2006), pp. 81-84.
  
  You can download this paper as a .pdf file.
  
  
  
• I. Rachunkova, O. Koch, G. Pulverer, E. B. Weinmüller, On a Singular Problem Arising in the Theory of Shallow Membrane Caps, J. Math. Anal. Appl. 332(2007), pp. 523-541.
  
  You can download this paper as a .pdf file.
  
  
  
• O. Koch, C. Lubich, Variational Splitting Time Integration of the MCTDHF Equations in Electron Dynamics, IMA J. Numer. Anal. 31 (2011), pp. 379-395.
  
  You can download this paper as a .pdf file.
  
  
  
• P. Blaha, H. Hofstätter, O. Koch, R. Laskowsky, K. Schwarz, Iterative Diagonalization in APW Based Methods in Electronic Structure Calculations, J. Comput. Phys. 229(2010), pp. 453-460.
  
  You can download this paper as a .pdf file.
  
  
  
• O. Koch, R. März, D. Praetorius, E. B. Weinmüller, Collocation Methods for Index 1 DAEs with a Singularity of the First Kind, Math. Comp. 79(2010), pp. 281-304.
  
  You can download this paper as a .pdf file.
  
  
  
• C. Ede, G. Jordan, O. Koch, A. Scrinzi, Hierarchical Matrices in Computations of Electron Dynamics, J. Sci. Comput. 42(2010), pp. 447-455.
  
  You can download this paper as a .pdf file.
  
  
  
• O. Koch, The Variational Splitting Method for the Multi-Configuration Time-Dependent Hartree-Fock Equations for Atoms, JNAIAM J. Numer. Anal. Indust. Appl. Math. 7(2012), pp. 1-13.
  
  You can download this paper as a .pdf file.
  
  
  
• G. Kitzhofer, O. Koch, G. Pulverer, Ch. Simon, and E. B. Weinmüller, The New Matlab Code bvpsuite for the Solution of Singular Implicit BVPs, JNAIAM J. Numer. Anal. Indust. Appl. Math. 5(2010), pp. 113-134.
  
  You can download this paper as a .pdf file.
  
  
  
• O. Koch, and C. Lubich, Dynamical Tensor Approximation, SIAM J. Matrix Anal. Appl. 31(2010), pp. 2360-2375.
  
  You can download this paper as a .pdf file.
  
  
  
• J. Cash, G. Kitzhofer, O. Koch, G. Moore, and E. B. Weinmüller, Numerical Solution of Singular Two Point BVPs, JNAIAM J. Numer. Anal. Indust. Appl. Math. 4(2009), pp. 129-149.
  
  You can download this paper as a .pdf file.
  
  
  
• O. Koch, C. Neuhauser, M. Thalhammer, Error Analysis of High-order Splitting Methods for Nonlinear Evolutionary Schrödinger Equations and Application to the MCTDHF Equations in Electron Dynamics, M2AN Math. Model. Numer. Anal. 47(2013), pp. 1265-1286.
  
  You can download this paper as a .pdf file.
  
  
  
• R. Hammerling, O. Koch, Ch. Simon, and E. B. Weinmüller, Numerical Solution of Singular ODE Eigenvalue Problems in Electronic Structure Computations, Comput. Phys. Commun. 181 (2010), pp. 1557-1561.
  
  You can download this paper as a .pdf file.
  
  
  
• O. Koch, C. Neuhauser, M. Thalhammer, Embedded Split-Step Formulae for the Time Integration of Nonlinear Evolution Equations, Appl. Numer. Math. 63(2013), pp. 14-24.
  
  You can download this paper as a .pdf file.
  
  
  
• N. Happenhofer, O. Koch, F. Kupka, and F. Zaussinger, Total variation diminishing implicit Runge--Kutta methods for dissipative advection-diffusion problems in astrophysics, PAMM, Proc. Appl. Math. Mech. 11(2011), pp. 777-778.
  
  You can download this paper as a .pdf file.
  
  
  
• F. Kupka, N. Happenhofer, I. Higueras, and O. Koch, Total-Variation-Diminishing Implicit-Explicit Runge-Kutta Methods for the Simulation of Double-Diffusive Convection in Astrophysics, J. Comput. Phys. 231(2012), pp. 3561-3586.
  
  You can download this paper as a .pdf file.
  
  
  
• A. Dick, O. Koch, R. März, and E. B. Weinmüller, Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point, Math. Comp. 82 (2013), pp. 893-918.
  
  You can download this paper as a .pdf file.
  
  
  
• I. Higueras, N. Happenhofer, O. Koch, and F. Kupka, Optimized Strong Stability Preserving IMEX Runge-Kutta Methods, J. Comput. Appl. Math. 272(2014), pp. 116-140.
  
  You can download a preprint of this article as a .pdf file.
  
  
  
• H. Hofstätter, O. Koch, and M. Thalhammer, Convergence analysis of high-order time-splitting pseudo-spectral methods for rotational Gross–Pitaevskii equations, Numer. Math. 127(2014), pp. 315-364.
  
  You can download a preprint of this article as a .pdf file. Archived at https://uscholar.univie.ac.at/.
  
  
  
• H. Hofstätter and O. Koch, An Approximate Eigensolver for Self-Consistent Field Calculations, Numer. Algorithms 66(2014), pp. 609-641.
  
  You can download a preprint of this article as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, M. Thalhammer, Defect-Based Local Error Estimators for Splitting Methods with Application to Schrödinger Equations, Part I. The Linear Case. J. Comput. Appl. Math. 236(2012), pp. 2643-2659.
  
  You can download a preprint of this paper as a .pdf file. Archived at https://uscholar.univie.ac.at/.
  
  
  
• P. Amodio, C.J. Budd, O. Koch, G. Settanni, E. B. Weinmüller, Asymptotical Computations for a Model of Flow in Concrete, Appl. Math. Comput. 237C(2014), pp. 155-167.
  
  You can download this paper as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, M. Thalhammer, Defect-Based Local Error Estimators for Splitting Methods with Application to Schrödinger Equations, Part II. Higher-Order Methods for Linear Problems, J. Comput. Appl. Math. 255(2014), pp. 384-403.
  
  You can download a preprint of this paper as a .pdf file. Archived at https://uscholar.univie.ac.at/.
  
  
  
• W. Auzinger, H. Hofstätter, O. Koch, and M. Thalhammer, Defect-Based Local Error Estimators for Splitting Methods, with Application to Schrödinger Equations, Part III. The Nonlinear Case, J. Comput. Appl. Math. 273(2014), pp. 182-204.
  
  You can download a preprint of this paper as a .pdf file. Archived at https://uscholar.univie.ac.at/.
  
  
  
• W. Auzinger, A. S. Bagherzadeh, and O. Koch. Error Estimation Based on Locally Weighted Defect for Boundary Value Problems in Second Order Ordinary Differential Equations, BIT Numer. Math. 54(2014), pp. 873-900.
  
  You can download a preprint of this paper as a .pdf file.
  
  
  
• F. Kupka, H. Grimm-Strele, N. Happenhofer, I. Higueras, O. Koch, and H. Muthsam. Improved Time Integration for WENO Methods in Astrophysical Applications, Series Numerical Modeling of Space Plasma Flows: ASTRONUM-2013. ASP Conference Series, Vol. 488. N.V. Pogorelov, E. Audit, and G.P. Zank, eds., 2014 Astronomical Society of the Pacific, pp. 243-248.
  
  You can download this paper as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, M. Thalhammer, Defect-Based Local Error Estimators for High-Order Splitting Methods Involving Three Linear Operators, Numer. Algorithms 70(2015), pp. 61-91.
  
  You can download a preprint of this paper as a .pdf file. Archived at https://uscholar.univie.ac.at/.
  
  
  
• W. Auzinger, Th. Kassebacher, O. Koch, M. Thalhammer, Adaptive Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Regime, Numer. Algorithms 72(2016), pp. 1-35.
  
  You can download a preprint of this paper as a .pdf file. Also available from http://arxiv.org/abs/1605.00429. Archived at https://uscholar.univie.ac.at.
  
  
  
• W. Auzinger, H. Hofstätter, D. Ketcheson, and O. Koch, Practical Splitting Methods for the Adaptive Integration of Nonlinear Evolution Equations. Part I: Construction of Optimized Schemes and Pairs of Schemes, BIT 57(2017), pp. 55-74, DOI=dx.doi.org/10.1007/s10543-016-0626-9.
  
  You can download a preprint of this paper as a .pdf file. Also available from http://arxiv.org/abs/1604.01179
  
  
  
• W. Auzinger, O. Koch, and M. Thalhammer, Representation of the Local Error for Higher-Order Exponential Splitting Schemes Involving Two or Three Sub-Operators, AIP Conference Proceedings 1648, DOI=dx.doi.org/10.1063/1.4912433.
  
  You can download a preprint of this paper as a .pdf file.
  
  
  
• W. Auzinger, W. Herfort, O. Koch, and M. Thalhammer, The BCH-Formula and Order Conditions for Splitting Methods, in: Lie Groups, Differential Equations, and Geometry, G. Falcone (ed.), UNIPA Springer Series, Vol. XIV(2017), pp. 71-84.
  
  
  
• W. Auzinger, O. Koch, and M. Quell, Adaptive High-Order Splitting Methods for Systems of Nonlinear Evolution Equations with Periodic Boundary Conditions, Numer. Algorithms 75(2017), pp. 261-283. DOI=dx.doi.org/10.1007/s11075-016-0206-8.
  
  You can download a preprint of this paper as a .pdf file. Also available from http://arxiv.org/abs/1604.01201
  
  
  
• W. Auzinger, Th. Kassebacher, O. Koch, M. Thalhammer, Convergence of a Strang Splitting Finite Element Discretization for the Schrödinger-Poisson Equation, M2AN - Math. Model. Numer. Anal. 51(2017), pp. 1245-1278. DOI=dx.doi.org/10.1051/m2an/2016059.
  
  You can download a reprint of this paper as a .pdf file. The original publication is available at www.esaim-m2an.org, the copyright is owned by EDP Sciences. Preprint also available from http://arxiv.org/abs/1605.00437
  
  
  
• W. Auzinger, H. Hofstätter, and O. Koch, Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators, Springer LNCS 9890(2016), pp. 43-57.
  
  You can download a preprint of this paper from http://arxiv.org/abs/1605.00453
  
  
  
• W. Auzinger, W. Herfort, H. Hofstätter, and O. Koch, Setup of Order Conditions for Splitting Methods, Springer LNCS 9890(2016), pp. 30-42.
  
  You can download a preprint of this paper from http://arxiv.org/abs/1605.00445
  
  
  
• W. Auzinger, H. Hofstätter, O. Koch, and M. Thalhammer, Reduced Order of the Local Error Of Splitting For Parabolic Problems with Dirichlet Boundary Conditions, in `Numerical Analysis and Applied Mathematics' AIP Conference Proceedings1863, 160008 (2017). DOI=dx.doi.org/10.1063/1.4992342
  
  
  
• C.J. Budd, O. Koch, L. Taghizadeh, and E. B. Weinmüller, Asymptotic properties of the space-time adaptive numerical solution of a nonlinear heat equation, Calcolo 55(2018), 43. DOI=dx.doi.org/10.1007/s10092-018-0286-z.
  
  You can download a preprint of this paper here.
  
  
  
• W. Auzinger, I. Brezinova, H. Hofstätter, O. Koch, and M. Quell, Practical Splitting Methods for the Adaptive Integration of Nonlinear Evolution Equations. Part II: Comparisons of Local Error Estimation and Step-Selection Strategies, Comput. Phys. Commun. 234(2019), pp. 55-71.
  
  You can download an extended preprint of this paper as a .pdf file. Archived at https://uscholar.univie.ac.at.
  
  
  
• S. Donsa, H. Hofstätter, O. Koch, J. Burgdörfer, and I. Brezinova, Long-time expansion of a Bose-Einstein condensate: Observability of Anderson localization, Phys. Rev. A 96, 043630 (2017).
  
  You can download a preprint from https://arxiv.org/abs/1707.02106.
  
  
  
• H. Hofstätter and O. Koch, Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four, Numer. Math. 141(2019), pp. 681-691.
  
  You can download a preprint of this paper from https://arxiv.org/abs/1709.08473
  
  
  
• W. Auzinger, H. Hofstätter, O. Koch, M. Quell, and M. Thalhammer, A posteriori error estimation for Magnus-type integrators, M2AN - Math. Model. Numer. Anal. 53(2019), pp. 197-218. DOI=https://doi.org/10.1051/m2an/2018050
  
  You can download a reprint of this paper as a .pdf file. The original publication is available at www.esaim-m2an.org, the copyright is owned by EDP Sciences. You can download an extended preprint of this paper as a .pdf file.
  
  
  
• W. Auzinger and O. Koch, An improved local error estimator for symmetric time-stepping schemes, Appl. Math. Lett. 82(2018), pp.106-110.
  
  Archived at https://uscholar.univie.ac.at/.
  
  
  
• W. Auzinger, I. Brezinova, H. Hofstätter, O. Koch, and T. Sato, Efficient adaptive exponential time integrators for nonlinear Schrödinger equations with nonlocal potential, Journal of Computational Mathematics and Data Science 1(2021), 100014.
  
  You can download this paper here.
  
  
  
• O. Koch, Convergence of exponential Lawson-multistep methods for the MCTDHF equations, M2AN - Math. Model. Numer. Anal. 53(2019), pp. 2109-2119. DOI=10.1051/m2an/2019033.
  
  You can download a reprint of this paper as a .pdf file. The original publication is available at www.esaim-m2an.org, the copyright is owned by EDP Sciences.
  
  
  
• W. Auzinger, H. Hofstätter, and O. Koch, Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations, J. Comput. Appl. Math. 234(2019), pp. 195-201. Available online from https://doi.org/10.1016/j.cam.2019.02.011.
  
  You can download a preprint of this paper from https://arxiv.org/abs/1806.07771
  
  
  
• T. Jawecki, W. Auzinger, and O. Koch, Computable upper bounds for Krylov approximations to matrix exponentials and associated φ-functions, BIT 60(2020), 157-197 BIT. DOI=10.1007/s10543-019-00771-6.
  
  You can download a preprint of this paper from https://arxiv.org/abs/1809.03369
  
  
  
• P. Amodio, C.J. Budd, O. Koch, V. Rottschäfer, G. Settanni, E. B. Weinmüller, Near critical, self-similar, blow-up solutions of the generalised Korteweg-de Vries equation: asymptotics and computations, Physica D 401(2020), 132179.
  
  You can download a preprint of this paper from http://www.asc.tuwien.ac.at/preprint/2019/asc02x2019.pdf
  
  
  
• W. Auzinger, H. Hofstätter, K. Kropielnicka, O. Koch, and P. Singh, Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime, Appl. Math. Comput. 362 (2019), 124550.
  
  You can download a preprint of this paper from https://arxiv.org/abs/1902.04324
  
  
  
• W. Auzinger, H. Hofstätter, and O. Koch Non-existence of generalized splitting methods with positive coefficients of order higher than four, Appl. Math. Lett. 97(2019), pp. 48-52. Available online from https://doi.org/10.1016/j.aml.2019.05.017.
  
  You can download a preprint of this paper from https://arxiv.org/abs/1905.05492.
  
  
  
• W. Auzinger, H. Hofstätter, and O. Koch, An algorithm for computing coefficients of words in expressions involving exponentials and its application to the construction of exponential integrators, Springer Lecture Notes in Computer Science 11661 (2019), pp. 197-214.
  
  You can download a preprint of this paper from https://arxiv.org/abs/1912.01399v1.
  
  
  
• W. Auzinger, A. Grosz, H. Hofstätter, and O. Koch, Adaptive exponential integrators for MCTDHF, Springer LNCS 11958 (2020), pp. 557-565.
  
  You can download a preprint of this paper from https://arxiv.org/abs/1905.05590.
  
  
  
• W. Auzinger, J. Dubois, K. Held, H. Hofstätter, T. Jawecki, A. Kauch, O. Koch, K. Kropielnicka, P. Singh, and C. Watzenböck, Efficient Magnus-type integrators for solar energy conversion in Hubbard models, Journal of Computational Mathematics and Data Science 2 (2021), pp. 100018.
  
  You can download this paper from https://doi.org/10.1016/j.jcmds.2021.100018.
  
  
  
• R. Wanzenböck, S. Donsa, H. Hofstätter, O. Koch, P. Schlagheck, I. Brezinova, Chaos-induced loss of coherence of a Bose-Einstein condensate, Phys. Rev. A 103, 023336.
  
  You can download a preprint of this paper from https://arxiv.org/abs/2007.07662.
  
  
  
• W. Auzinger, H. Hofstätter, O. Koch, and M. Quell, Adaptive time propagation for time-dependent Schrödinger equations, Int. J. Appl. Comput. Math. 7 (2020), pp. 6.
  
  This paper is available from https://doi.org/10.1007/s40819-020-00937-9.
  
  
  
• W. Auzinger, T. Jawecki, O. Koch, P. Pukach, R. Stolyarchuk, and E. B. Weinmüller, Some aspects on [numerical] stability of evolution equations of stiff type; use of computer algebra, Proceedings of MEMSTECH 2021, pp. 180-184.
  
  
  
• W. Auzinger, L. Einramhof K. Held, A. Kauch, O. Koch, and C. Watzenböck, Efficient adaptive computation of the dynamics of Mott transistors, to appear in AIP Conference Proceedings.
  
  
  
• W. Auzinger, K. Burdeos, M. Fallahpour, O. Koch, R. Mendoza, and E. B. Weinmüller, A numerical continuation method for parameter-dependent boundary value problems using bvpsuite 2.0, JNAIAM J. Numer. Anal. Indust. Appl. Math. 16(2022), pp. 1-13.
  
  You can download this paper from http://www.jnaiam.org/index.php?/categories/62-Issues-1-2.
  
  
  
• O. Koch, K. Acar, W. Auzinger, F. Kupka, and B. Moser, Adaptive exponential multi-operator splitting for MHD, submitted.
  
  You can download a preprint of this paper from https://arxiv.org/abs/2302.01092.
  
  
  Other Publications
  
  
• O. Koch, P. Kofler, E. B. Weinmüller, Analysis of Singular Initial and Terminal Value Problems, Technical Report 125/99, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 1999.
  
  You can view the abstract of this technical report or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, P. Kofler, E. B. Weinmüller, The Application of Shooting to Singular Boundary Value Problems, Technical Report 126/99, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 1999.
  
  You can view the abstract of this technical report or download the entire text as a .pdf file.
  
  
  
• O. Koch, E. B. Weinmüller, Acceleration Techniques for Singular Initial Value Problems, in: Problems in Modern Applied Mathematics (N. Mastorakis, ed.), World Scientific and Engineering Society Press, 2000, pp. 6-11.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, P. Kofler, E. B. Weinmüller, Acceleration Techniques for Singular Initial Value Problems, Technical Report 129/00, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2000.
  
  You can view the abstract of this technical report or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, W. Polster, E. B. Weinmüller, Ein Algorithmus zur Gittersteuerung bei Kollokationsverfahren für singuläre Randwertprobleme, Technical Report ANUM Preprint 21/01, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2001.
  
  You can download the entire text of this technical report as a .pdf file.
  
  
  
• W. Auzinger, G. Kneisl, O. Koch, W. Polster E. B. Weinmüller, Implementation of a Solution Routine for Singular Boundary Value Problems, in Seminarbericht S70 MATLAB/SIMULINK: Einsatz, Anwendungen, Entwicklungen. ARGESIM - Working Group Simulation News, 2001.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, G. Kneisl, O. Koch, E. B. Weinmüller, A Solution Routine for Singular Boundary Value Problems, Technical Report ANUM Preprint 1/02, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2002.
  
  You can view the abstract of this technical report or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, G. Kneisl, O. Koch, E. B. Weinmüller, SBVP 1.0 - A MATLAB Solver for Singular Boundary Value Problems, ANUM Preprint Nr. 2/02, Vienna University of Technology, Austria, 2002.
  
  You can download this manual as a .pdf file. The software described in this document is available here.
  
  
  
• W. Auzinger, O. Koch, S. Lammer, E. B. Weinmüller, Variationen der Defektkorrektur zur effizienten numerischen Lösung gewöhnlicher Differentialgleichungen, Technical Report ANUM Preprint 8/02, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2002.
  
  You can download the entire text of this technical report as a .pdf file.
  
  
  
• O. Koch, A. Paul, A. Traxler, E. B. Weinmüller, Efficient Numerical Solution of a Singular Initial Value Problem in Avalanche Modeling, Technical Report ANUM Preprint 11/02, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2002.
  
  You can view the abstract of this technical report or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, J. Petrickovic, E. B. Weinmüller, Numerical Solution of Boundary Value Problems with an Essential Singularity, Technical Report ANUM Preprint 3/03, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2003.
  
  You can download the entire text as a .pdf file.
  
  
  
• H. Hofstätter, O. Koch, Splitting Defect Correction, Technical Report AURORA TR2003-23, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2003.
  
  You can download the entire text as a .pdf file.
  
  
  
• O. Koch, W. Kreuzer, A. Scrinzi, MCTDHF in Ultrafast Laser Dynamics, Technical Report AURORA TR2003-29, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2003.
  
  You can download the entire text as a .pdf file.
  
  
  
• H. Hofstätter, O. Koch, Defect Correction for Geometric Integrators, Proceedings of Aplimat 2004, pp. 465-470.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, H. Hofstätter, O. Koch, W. Kreuzer, E. B. Weinmüller, Superconvergent Defect Correction Algorithms, WSEAS Transactions on Systems, 4(2004), pp. 1378-1383.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• O. Koch, Numerical Solution of the Time-Dependent Schrödinger Equation in Ultrafast Laser Dynamics, WSEAS Trans. Math. 3(2004), pp. 584-590.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  
  
  
• W. Auzinger, E. Karner, O. Koch, D. Praetorius, E. B. Weinmüller, Globale Fehlerschätzer für Randwertprobleme mit einer Singularität der zweiten Art, Technical Report ANUM Preprint 6/03, Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria, 2003.
  
  You can download the entire text as a .pdf file.
  
  
  
• C.J. Budd, O. Koch, E. B. Weinmüller, From the Nonlinear Schrödinger Equation to Singular BVPs, Technical Report AURORA TR2004-02, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004.
  
  You can download the entire text as a .pdf file.
  
  
  
• C.J. Budd, O. Koch, E. B. Weinmüller, Self-Similar Blow-Up in Nonlinear PDEs, Technical Report AURORA TR2004-15, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004.
  
  You can download the entire text as a .pdf file.
  
  
  
• H. Hofstätter, O. Koch, Convergence Proof for Iterated Splitting Defect Correction, Technical Report AURORA TR2004-05, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004.
  
  You can download the entire text as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, D. Praetorius, G. Pulverer, E. B. Weinmüller, Performance of Collocation Software for Singular BVPs, Technical Report ANUM Preprint 4/04, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004.
  
  You can download the entire text as a .pdf file.
  
  
  
• G. Kitzhofer, O. Koch, E. B. Weinmüller, Kollokationsverfahren für singuläre Randwertprobleme zweiter Ordnung in impliziter Form, Technical Report ANUM Preprint 9/04, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004. Also available as AURORA TR2004-13.
  
  You can download the entire text as a .pdf file.
  
  
  
• W. Kreuzer, O. Koch, Performance of MCTDHF Implementations, Technical Report AURORA TR2004-14, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004.
  
  You can download the entire text as a .pdf file.
  
  
  
• G. Kitzhofer, O. Koch, E. B. Weinmüller, Collocation Methods for the Computation of Bubble-Type Solutions of a Singular BVP in Hydrodynamics, Technical Report ANUM Preprint 14/04, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004.
  
  You can download the entire text as a .pdf file.
  
  
  
• O. Koch, Approximation Methods in Multi-Particle Quantum Dynamics, poster presentation at Stipendiatenwochenende of the Austrian Academy of Sciences, March 31^st 2006.
  
  You can download the poster as a .pdf file.
  
  
  
• G. Kitzhofer, O. Koch, E. B. Weinmüller, Pathfollowing for Essentially Singular Boundary Value Problems with Application to the Complex Ginzburg-Landau Equation, ASC Report No. 19/07, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2007.
  
  You can download the entire text as a .pdf file.
  
  
  
• O. Koch, R. März, D. Praetorius, and E. B. Weinmüller, Collocation for Solving DAEs with Singularities, ASC Report No. 32/2007, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2007.
  
  You can download the entire text as a .pdf file.
  
  
  
• O. Koch, C. Lubich, Analysis and Time Integration of the Multi-Configuration Time-Dependent Hartree-Fock Equations in Electron Dynamics, ASC Report No. 04/2008, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2008.
  
  You can download the entire text as a .pdf file.
  
  
  
• O. Koch, Approximation of the Meanfield Terms in MCTDHF Computations by H-Matrices, ASC Report No. 05/2008, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2008.
  
  You can download the entire text as a .pdf file.
  
  
  
• O. Koch, C. Lubich, Time Propagation of the MCTDHF Equations in Electron Dynamics, poster presentation at the Second Workshop on High-Dimensional Quantum Dynamics, La Grande Motte, France, 2008.
  
  You can download the poster as a .pdf file.
  
  
  
• O. Koch, R. März, D. Praetorius, and E. B. Weinmüller, Collocation Methods for Index 1 DAEs with a Singularity of the First Kind, ASC Report No. 10/2008, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2008.
  
  You can download this report as a .pdf file.
  
  
  
• J. Cash, G. Kitzhofer, O. Koch, G. Moore, and E. B. Weinmüller, Numerical Solution of Singular Two Point BVPs, ASC Report No. 22/2008, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2008.
  
  You can download this report as a .pdf file.
  
  
  
• O. Koch, E. B. Weinmüller, Numerical Treatment of Singular BVPs: The New MATLAB Code bvpsuite, ASC Report No. 09/2009, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2009.
  
  You can download this report as a .pdf file.
  
  
  
• G. Kitzhofer, O. Koch, G. Pulverer, Ch. Simon, and E. B. Weinmüller, bvpsuite: A New MATLAB Solver for Singular Implicit Boundary Value Problems, ASC Report No. 35/2009, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2009.
  
  You can download this report as a .pdf file.
  
  
  
• G. Kitzhofer, O. Koch, G. Pulverer, Ch. Simon, and E. B. Weinmüller, The New MATLAB Code bvpsuite for the Solution of Singular Implicit BVPs, ASC Report No. 03/2010, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2010.
  
  You can download this report as a .pdf file.
  
  
  
• R. Hammerling, O. Koch, C. Simon, and E. B. Weinmüller, Numerical Solution of Singular ODE Eigenvalue Problems in Electronic Structure Computations, ASC Report No. 07/2010, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2010.
  
  You can download this report as a .pdf file.
  
  
  
• R. Hammerling, O. Koch, C. Simon, and E. B. Weinmüller, Numerical Solution of Singular Eigenvalue Problems for ODEs with a Focus on Problems Posed on Semi-Infinite Intervals, ASC Report No. 08/2010, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2010.
  
  You can download this report as a .pdf file.
  
  
  
• A. Dick, O. Koch, R. März, and E. B. Weinmüller, Convergence of Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point, ASC Report No. 13/2010, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2010.
  
  You can download this report as a .pdf file.
  
  
  
• R. Hammerling, O. Koch, C. Simon, and E. B. Weinmüller, Numerical Treatment of Singular ODE EVPs Using bvpsuite, ASC Report No. 16/2010, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2010.
  
  You can download this report as a .pdf file.
  
  
  
• R. Hammerling, J. Kamleitner, and O. Koch, Numerical Methods in Quantum Propagation, ASC Report No. 19/2010, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2010.
  
  You can download this report as a .pdf file.
  
  
  
• O. Koch, F. Kupka, B. Löw-Baselli, A. Mayrhofer, and F. Zaussinger, SDIRK methods for the ANTARES code, ASC Report No. 32/2010, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2010.
  
  You can download this report as a .pdf file.
  
  
  
• N. Happenhofer, O. Koch, and F. Kupka, IMEX methods for the ANTARES code, ASC Report No. 27/2011, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2011.
  
  You can download this report as a .pdf file.
  
  
  
• I. Higueras, N. Happenhofer, O. Koch, and F. Kupka, "Optimized IMEX Runge-Kutta methods for simulations in astrophysics: A detailed study", ASC Report No. 14/2012, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2012.
  
  You can download this report as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, M. Schöbinger, and E. B. Weinmüller, A new version of the code bvpsuite for singular BVPs in ODEs: Nonlinear solver and its application to m-Laplacians, ASC Report No. 28/2015, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2015.
  
  You can download this report as a .pdf file.
  
  
  
• O. Koch, S. Schirnhofer, and E. B. Weinmüller, Numerical simulation of the Korteweg-de Vries Equation for shallow water waves, ASC Report No. 34/2015, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2015.
  
  You can download this report as a .pdf file.
  
  
  
• W. Auzinger, O. Koch, E. B. Weinmüller, and S. Wurm Modular version bvpsuite1.2 of the collocation MATLAB package bvpsuite1.1, ASC Report No. 30/2019, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2019.
  
  You can download this report as a .pdf file.
  
  
  
• W. Auzinger, M. Fallahpour, O. Koch, and E. B. Weinmüller, Implementation of a pathfollowing strategy with an automatic step-length control: New MATLAB package bvpsuite2.0, ASC Report No. 31/2019, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2019.
  
  You can download this report as a .pdf file.
  
  
  Talks at International Conferences
  
  
• O. Koch, Analysis and Numerical Treatment of Singular Initial Value Problems, ANODE 98 - Auckland Numerical ODEs, Auckland, New Zealand, June/July 1998. Joint with P. Kofler and E. B. Weinmüller.
  
  You can view the abstract of this talk I gave on July 3^rd 1998.
  
  
  
• O. Koch, The Convergence of Shooting Methods for Singular Boundary Value Problems, 18^th Biennial Conference on Numerical Analysis, Dundee, Scotland, June/July 1999. Joint with E. B. Weinmüller.
  
  You can view the abstract of this talk I gave on June 29^th 1999.
  
  
  
• O. Koch, Acceleration Techniques for Singular Initial Value Problems, 4^th World Multi-Conference on Circuits, Systems, Communication and Computers, Athens, Greece, July 2000. Joint with E. B. Weinmüller.
  
  You can view the abstract of this invited talk I gave on July 11^th 2000.
  
  
  
• O. Koch, Efficient Collocation Schemes for Singular Boundary Value Problems, ANODE 2001 - Auckland Numerical ODEs, Auckland, New Zealand, January 2001. Joint with W. Auzinger and E. B. Weinmüller.
  
  You can view the abstract of this talk I gave on January 11^th 2001.
  
  
  
• O. Koch, A Collocation Solver for Singular Boundary Value Problems, SciCADE 2001 - International Conference on Scientific Computation and Differential Equations, Vancouver, Canada, July/August 2001. Joint with W. Auzinger, G. Kneisl and E. B. Weinmüller.
  
  You can view the abstract of this talk I gave on July 31 ^st 2001.
  
  
  
• O. Koch, Theory, Solution Techniques and Applications of Singular Boundary Value Problems for Ordinary Differential Equations, PPAM 2001 - 4^th International Conference on Parallel Processing and Applied Mathematics, Naleczow, Poland, September 2001. Joint with W. Auzinger and E. B. Weinmüller.
  
  You can view the abstract of this invited talk I gave on September 11^th 2001.
  
  
  
• O. Koch, Effiziente Lösung von Singulären Differentialgleichungen, 15. ÖMG-Kongress, Vienna, Austria, September 2001. Joint with W. Auzinger, and E. B. Weinmüller.
  
  You can view the abstract of this talk I gave on September 20^th 2001.
  
  
  
• O. Koch, New Variants of Defect Correction for Boundary Value Problems in ODEs, Part II, ICM 2002, Xi'an, China, August 2002. Joint with W. Auzinger and E. B. Weinmüller.
  
  You can view the abstract of this talk I gave on August 16^th 2002.
  
  
  
• O. Koch, A Posteriori Error Estimation for Collocation Methods Applied to Singular Boundary Value Problems, Part II, SciCADE 2003 - International Conference on Scientific Computation and Differential Equations, Trondheim, Norway, June/July 2003. Joint with E. B. Weinmüller.
  
  You can view the abstract of this talk I gave on July 3^rd 2003.
  
  
  
• O. Koch, Asymptotically Correct Error Estimation for Collocation Methods Applied to Singular Boundary Value Problems, ANODE 2003 - Auckland Numerical ODEs, Auckland, New Zealand, July 2003.
  
  You can view the abstract of this talk I gave on July 18^th 2003.
  
  
  
• O. Koch, Modeling Ambulance Service of the Austrian Red Cross, Winter Simulation Conference 2003, New Orleans, USA, December 2003. Joint with H. Weigl.
  
  
  
• O. Koch, Computation of Self-Similar Solution Profiles for the Nonlinear Schrödinger Equation, ICCAM 2004, Leuven, Belgium, July 2004. Joint with C.J. Budd and E. B. Weinmüller.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Numerical Solution of the Time-Dependent Schrödinger Equation in Ultrafast Laser Dynamics, NAA'04, Corfu, Greece, August 2004.
  
  
  
• O. Koch, Software for Singular Boundary Value Problems, International Workshop on Analysis and Numerical Approximation of Singular Problems, Lisbon, Portugal, November 2004. Joint with W. Auzinger and E. B. Weinmüller.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Pathfollowing for Multi-Bump Solutions of the Complex Ginzburg-Landau Equation, SciCADE 2005 - International Conference on Scientific Computation and Differential Equations, Nagoya, Japan, May 2005. Joint with G. Kitzhofer and E. B. Weinmüller.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Analytical and Numerical Treatment of the MCTDHF Approximation to the Time-Dependent Schrödinger Equation, Conference on Differential and Difference Equations, Gdansk, Poland, August 2005.
  
  
  
• O. Koch, Theory and Computation of the MCTDHF Approximation for the Time-Dependent Schrödinger Equation, 3rd Austrian NA Day, Vienna, Austria, April 2007.
  
  
  
• O. Koch, Numerical Solution of Singular Boundary Value Problems in Ordinary Differential Equations, 1st Austrian-Mongolian Mathematics Day, Vienna University of Technology, Vienna, Austria, October 2007. Joint with W. Auzinger and E. B. Weinmüller.
  
  
  
• O. Koch, Analysis and Numerical Approximation of the Multi-Configuration Time-Dependent Hartree-Fock Equations, 24th GAMM Seminar Leipzig on Tensor Approximations, Leipzig, Germany, January 2008. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Variational Approximations in Linear Algebra and Quantum Dynamics, 79th Annual GAMM Conference, Bremen, Germany, April 2008. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Time Integration of the Multi-Configuration Time-Dependent Hartree-Fock Equations, 4th Austrian NA Day, Linz, Austria, April 2008. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Dynamical Low Rank Approximation of Tensors, ICCAM 2008 13th International Congress on Computational and Applied Mathematics, Ghent, Belgium, July 2008. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Mathematical and Numerical Analysis of the MCTDH Equations in Quantum Dynamics, Numerical Methods in Density Functional Theory, Berlin, Germany, July 2008. Joint with C. Lubich.
  
  You can view the abstract of this invited keynote lecture here.
  
  
  
• O. Koch, Splitting Methods for the Multi-Configuration Time-Dependent Hartree-Fock Equations, SDIDE - Stability and Discretization Issues in Differential Equations, Vienna, Austria, September 2008. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, The Variational Splitting Method for the Multi-Configuration Time-Dependent Hartree-Fock Equations, Splitting Methods in Time Integration, Innsbruck, Austria, October 2008. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Numerical Computation of the Multi-Particle Time-Dependent Schrödinger Equation, International Workshop on Semiconductor Devices: Analysis, Simulations, Applications, Beijing, China, April 2009. Joint with C. Lubich.
  
  You can view the abstract of this invited talk here.
  
  
  
• O. Koch, Dynamical Low Rank Approximation for Higher-Order Tensors, 5th Austrian Numerical Analysis Day, Innsbruck, Austria, May 2009. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Split-Step Time Propagation of the Multi-Configuration Time-Dependent Hartree-Fock Equations for Atoms, 24th Biennial Conference on Numerical Analysis, Glasgow, U.K., June 2009. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Analysis of a Dynamical Low Rank Approximation for Tensors, ENUMATH 2009, Uppsala, Sweden, July 2009. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Variational Approximations in Quantum Dynamics and Multilinear Algebra, ÖMG Congress/ DMV Conference 2009, Graz, Austria, September 2009. Joint with C. Lubich.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Efficient High-Order Variational Splitting Methods for the MCTDHF Equations in Electron Dynamics, Workshop Two Days on Splitting Methods, Innsbruck, Austria, April 2010. Joint with C. Lubich, C. Neuhauser, and M. Thalhammer,
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Efficient High-Order Splitting Methods for the MCTDHF Equations, 6^thAustrian Numerical Analysis Day 2010, Salzburg, Austria, May 2010. Joint with C. Lubich, C. Neuhauser, and M. Thalhammer,
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Efficient High-Order Splitting Methods for Nonlinear Evolution Equations, BIT 50 Conference, Lund, Sweden, June 2010. Joint with C. Lubich, C. Neuhauser, and M. Thalhammer,
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, High-Order Structure-Preserving Discretization Methods for Nonlinear Evolution Equations, Workshop on Innovative Integrators, Innsbruck, Austria, October 2010. Joint with F. Kupka, C. Neuhauser, and M. Thalhammer,
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, High-Order Structure-Preserving Discretization Methods for Nonlinear Evolution Equations, Austrian-Chinese Workshop on Dissipative Systems: Kinetic Theory and Semiconductor Applications, Vienna, Austria, November 2010. Joint with F. Kupka, C. Neuhauser, and M. Thalhammer,
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Total Variation Diminishing Implicit Runge-Kutta Methods for Dissipative Advection-Diffusion Problems in Astrophysics, 82^nd GAMM Conference, Graz, Austria, April 2011. Joint with F. Kupka, A. Mayerhofer, and F. Zaussinger,
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Total-Variation Diminishing Runge-Kutta Methods for Advection-Diffusion Equations in Astrophysics, 1^st International Workshop on Small Scale Solar Magnetic Fields, Bairisch-Kölldorf, Austria, April 2011. Joint with N. Happenhofer, F. Kupka, A. Mayerhofer, and F. Zaussinger.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Total Variation Diminishing Implicit-Explicit Runge-Kutta Methods for Simulations of Semiconvection in Astrophysics, 7^th Austrian Numerical Analysis Day, Klagenfurt, Austria, May 2011. Joint with N. Happenhofer and F. Kupka.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Total Variation Diminishing Runge-Kutta Time Integrators for Dissipative Flow Problems in Astrophysics, ICNAAM 2011, Halkidiki, Greece, September 2011. Joint with N. Happenhofer, F. Kupka, and F. Zaussinger.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Error Estimators for Adaptive Splitting Methods, ÖMG Kongress 2011, Krems, Austria, September 2011. Joint with W. Auzinger, C. Neuhauser, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Adaptive Full Discretization of Nonlinear Schrödinger Equations, 8^thAustrian Numerical Analysis Day, Vienna, Austria, May 2012. Joint with W. Auzinger, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Adaptive Full Discretization of Gross-Pitaevskii Equations with Rotation Term, Workshop on Innovative Time Integration, Innsbruck, Austria, May 2012. Joint with W. Auzinger, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, An Approximate Eigensolver for Self-Consistent Field Calculations, 9^th Austrian Numerical Analysis Day, Graz, Austria, April 2013. Joint with H. Hofstätter.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Adaptive High-order Splitting Methods for Schrödinger Equations, SDIDE 2013 - Stability and Discretization Issues in Differential Equations, Pamplona, Spain, April 2013. Joint with W. Auzinger, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Local Estimates of the Time-Stepping Error for High-Order Splitting Methods, 25th Biennial Numerical Analysis Conference, Glasgow, U.K., June 2013. Joint with W. Auzinger, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Analysis of High-Order Adaptive Full Discretization for Nonlinear Schrödinger Equations, Functional Differential Equations, Gdansk, Poland, September 2013. Joint with W. Auzinger, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Fully Discrete Splitting Methods for Rotating Bose-Einstein Condensates, 18th ÖMG Congress and Annual DMV Meeting, Innsbruck, Austria, September 2013. Joint with W. Auzinger, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Parallel Adaptive Splitting Methods for Nonlinear Evolution Equations, 10th Austrian Numerical Analysis Day, Vienna, Austria, May 2014. Joint with W. Auzinger, H. Hofstätter, B. Muite, M. Quell, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Parallel Adaptive Splitting Methods for Nonlinear Evolution Equations, International Workshop on Algorithms and Software for Scientific Computing, Vienna, Austria, July 2014. Joint with W. Auzinger, H. Hofstätter, B. Muite, M. Quell, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Adaptive High-order Time-Splitting Methods for Systems of Evolution Equations. Applications in Quantum Dynamics and Pattern Formation, SciCADE - International Conference on Scientific Computing and Differential Equations 2015, Potsdam, Germany, September 2015. Joint with W. Auzinger, H. Hofstätter, Th. Kassebacher, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Time-splitting FEM discretization of the Schrödinger-Poisson equation, 12th Austrian Numerical Analysis Day, Innsbruck, April 2016. Joint with W. Auzinger, Th. Kassebacher, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Reduced Order of the Local Error of Splitting for Parabolic Problems, ICNAAM 2016, Rhodes, Greece, September 2016. Joint with W. Auzinger, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Error Analysis of Splitting Methods for Parabolic Problems under Dirichlet Boundary Conditions, 9th Workshop Numerical Analysis of Evolution Equations, Innsbruck, November 2016. Joint with W. Auzinger, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Adaptive Time-splitting FEM discretization of the Schrödinger-Poisson equation, Modern Numerical Methods for Quantum Mechanics, Warsaw, March 2017. Joint with W. Auzinger, Th. Kassebacher, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Adaptive exponential splitting and Lawson methods for Schrödinger equations, SciCADE 2017, Bath, U.K., September 2017. Joint with W. Auzinger, I. Brezinova, H. Hofstätter, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Adaptive exponential Lawson methods for nonlinear Schrödinger equations, 14th Austrian Numerical Analysis Day 2018, Klagenfurt, May 2018. Joint with W. Auzinger, I. Brezinova, and H. Hofstätter.
  
  
  
• O. Koch, Adaptive Magnus-type integrators for the simulation of solar cells, ICNAAM 2018, Rhodes, Greece. Joint with W. Auzinger, H. Hofstätter, M. Quell, and M. Thalhammer.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Efficient adaptive time integrators for high-dimensional Schrödinger equations, NSIDE - Workshop on Numerical Solution of Integral and Differential Equations, Gdansk, Poland, July 2019. Joint with W. Auzinger, A. Grosz, and H. Hofstätter.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, Adaptive exponential methods, SciCADE 2019 - Conference on Scientific Computing and Differential Equations, Innsbruck, July 2019. Joint with W. Auzinger, H. Hofstätter, T. Jawecki, K. Kropielnicka, and P. Singh.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch, joint with K. Acar, W. Auzinger, D. Hoffmann, F. Kupka, and B. Moser, Adaptive exponential multi-operator splitting for MHD, Austrian Numerical Analysis Day 2023, Vienna, April 2023.
  
  You can view the abstract of this talk here.
  
  
  
• O. Koch (invited talk), Low-rank Approximation of Time-dependent Tensors and Wave-functions, Dynamical Low-rank Approximation - New Horizons, Lausanne, Switzerland, May 2023.
  
  
  Invited Colloquium Talks
  
  
• O. Koch, Numerische Lösung von singulären Differentialgleichungen, University of Tübingen, Germany, June 2004.
  
  
  
• O. Koch, The Time-Dependent Multi-Particle Schrödinger Equation and Dynamical Low Rank Approximation, Humboldt University Berlin, Germany, November 2005.
  
  
  
• O. Koch, MCTDHF: A Model Reduction Technique for Computational Quantum Dynamics, Vienna University of Technology, Austria, March 2006.
  
  
  
• O. Koch, Numerical Treatment of the Multi-Particle Time-Dependent Schrödinger Equation, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, June 2007.
  
  
  
• O. Koch, Acceleration Techniques Adapted for Geometric Integrators, University of Tübingen, Germany, June 2007. Joint with H. Hofstätter.
  
  
  
• O. Koch, Numerical Integration of Nonlinear Schrödinger Equations, Wissenswertes aus der Mathematik, Vienna University of Technology, Austria, May 2008.
  
  
  
• O. Koch, Dynamical Low Rank Approximation of Matrices and Tensors, Jacobs University Bremen, Germany, September 2008.
  
  
  
• O. Koch, Analysis of a Defect Correction Method for Geometric Integrators, Innsbruck University, Austria, August 2009.
  
  
  
• O. Koch, Dynamical Tensor Approximation and Quantum Dynamics, Innsbruck University, Austria, October 2009.
  
  
  
• O. Koch, Total-Variation Diminishing Runge-Kutta Methods for Advection-Diffusion Equations in Astrophysics, Innsbruck University, Austria, March 2011.
  
  
  
• O. Koch, Adaptive Full Discretization of Nonlinear Schrödinger Equations, University of Tübingen, Germany, October 2013.
  
  
  
• O. Koch. Computing Nonlinear Evolution Equations, University of Bath, U.K., November 2013.
  
  
  
• O. Koch, Adaptive Numerical Methods for Nonlinear Evolution Equations, University of Tübingen, Germany, June 2015.
  
  
  
• O. Koch, Adaptive Full Discretization for Nonlinear Evolution Equations, Innsbruck University, Austria, December 2015.
  
  
  
• O. Koch, Adaptive Full Discretization for Nonlinear Evolution Equations, University of Bath, U.K., April 2016.
  
  
  
• O. Koch, Adaptivity for Splitting Schemes for Nonlinear Schrödinger Equations, University of Innsbruck, Innsbruck, July 2017.
  
  
  
• O. Koch, Adaptive Exponential Integrators for Schrödinger Equations, University of Gdansk, Gdansk, November 2017.
  
  
  Appointment-Related Talks
  
  
• O. Koch, The MCTDHF Approximation to the Time-Dependent Schrödinger Equation, University of Birmingham, U.K., August 2005.
  
  
  
• O. Koch, A Model Reduction Technique for the Time-Dependent Schrödinger Equation, University of Strathclyde, Glasgow, U.K., October 2005.
  
  
  
• O. Koch, Variational Approximations in Quantum Dynamics and in Linear Algebra, Heriot-Watt University Edinburgh, U.K., January 2006.
  
  
  
• O. Koch, Numerical Computation of Electron Dynamics, Durham University, U.K., February 2006.
  
  
  
• O. Koch, Dynamical Tensor Approximation and Quantum Dynamics, University of Bonn, Germany, October 2009.
  
  
  
• O. Koch, Adaptive High-Order Splitting Methods for Nonlinear Schrödinger Equations, University of Köln, Germany, June 2010.
  
  
  
• O. Koch, Efficient Numerical Approximation of High-Dimensional Evolution Equations, Humboldt University Berlin, Germany, December 2010.
  
  
  
• O. Koch, Efficient Numerical Approximation of High-Dimensional Evolution Equations, Albert-Ludwigs-Universität Freiburg, Germany, February 2011.
  
  
  
• O. Koch, Efficient Time Propagators for High-Dimensional Quantum Dynamics, Alpen-Adria University Klagenfurt, Austria, April 2011.
  
  
  
• O. Koch, Model Reduction Techniques for the Simulation of High- Dimensional Quantum Dynamics, Universität Stuttgart, Germany, May 2011.
  
  
  
• O. Koch, Adaptive Simulation of High-Dimensional Quantum Dynamics, Freie Universität Berlin, Germany, October 2011.
  
  
  
• O. Koch, Adaptive Split-Step Time Integrators for Quantum Dynamics, Technische Universität Chemnitz, Germany, February 2012.
  
  
  
• O. Koch, Adaptive Solution of Nonlinear Evolution Equations, Universität Osnabrück, Germany, April 2012.
  
  
  
• O. Koch, Approximation of High-Dimensional Quantum Dynamics, Universität Salzburg, Austria, November 2012.
  
  
  
• O. Koch, Adaptive Full Discretization of Nonlinear Schrödinger Equations, Universität Köln, Germany, December 2012.
  
  
  
• O. Koch, Adaptive Full Discretization of Nonlinear Schrödinger Equations, Leibniz Universität Hannover, Germany, December 2012.
  
  
  
• O. Koch, Adaptive Discretization Methods for Nonlinear Evolution Equations with Application to Rotating Bose-Einstein Condensates, Karl von Ossietzky Universität Oldenburg, Germany, January 2013.
  
  
  
• O. Koch, Adaptive Numerical Methods for Quantum Propagation, Universität Heidelberg, Germany, October 2013.
  
  
  
• O. Koch, Partitioned Time Integrators for Nonlinear Evolution Equations, Universität Bayreuth, Germany, April 2014.
  
  
  
• O. Koch, Adaptive numerische Verfahren für die Quantendynamik, Universität Paderborn, Germany, June 2014.
  
  
  
• O. Koch, Adaptive numerische Methoden für nichtlineare Evolutionsgleichungen, Ludwig-Maximilians-Universität München, Germany, November 2014.
  
  
  
• O. Koch, Adaptive Numerical Methods for Nonlinear Evolution Equations, Otto-von-Guericke-Universität Magdeburg, Germany, June 2015.
  
  
  
• O. Koch, Adaptive Numerical Methods for Nonlinear Evolution Equations, Universität Heidelberg, Germany, October 2015.

Co-Authored Talks

P. Kofler, The Application of Shooting to Singular Boundary Value Problems, 18^th Biennial Conference on Numerical Analysis, Dundee, Scotland, June/July 1999. Joint with W. Auzinger, O. Koch, E. B. Weinmüller.

You can view the abstract of this talk Peter Kofler gave on June 29^th 1999.

E. B. Weinmüller, The Application of Multiple Shooting to Singular Boundary Value Problems, SciCADE 99 - International Conference on Scientific Computing and Differential Equations, Fraser Island, Queensland, Australia, August 1999. Joint with W. Auzinger, O. Koch, P. Kofler.

You can view the abstract of this talk Ewa Weinmüller gave on August 12^th 1999.

E. B. Weinmüller, Error Estimate and Grid Selection for Singular Boundary Value Problems, Scientific Colloquium on Numerical Analysis of Differential Equations (in Honour of Roswitha März's 60^th Birthday), Berlin, Germany, October 2000. Joint with W. Auzinger, O. Koch (invited talk).

G. Kneisl, Implementation of a Solution Routine for Singular Boundary Value Problems, Seminar S70 MATLAB/SIMULINK: Einsatz, Anwendungen, Entwicklungen, ARGESIM - Working Group Simulation News, Vienna, Austria, May 2001. Joint with W. Auzinger, O. Koch, W. Polster and E. B. Weinmüller.

E. B. Weinmüller, A Collocation Code for Singular/Regular Boundary Value Problems, International Conference on Numerical Algorithms, Marrakesh, Morocco, October 2001. Joint with W. Auzinger, G. Kneisl, O. Koch.

You can view the abstract of this talk Ewa Weinmüller gave on October 1^st 2001.

E. B. Weinmüller, New Variants of Defect Correction for Boundary Value Problems in ODEs, Part I, ICM 2002, Xi'an, China, August 2002. Joint with W. Auzinger, O. Koch.

You can view the abstract of this talk Ewa Weinmüller gave on August 16^th 2002.

E. B. Weinmüller, The Numerical Solution of Boundary Value Problems with an Essential Singularity, 4^th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria, June 2003. Joint with W. Auzinger, O. Koch, J. Petrickovic.

You can view the abstract of this talk Ewa Weinmüller gave in June 2003.

E. B. Weinmüller, A Posteriori Error Estimation for Collocation Methods Applied to Singular Boundary Value Problems, Part I, SciCADE 2003 - International Conference on Scientific Computation and Differential Equations, Trondheim, Norway, June/July 2003. Joint with O. Koch.

You can view the abstract of this talk Ewa Weinmüller gave on July 3^rd 2003.

E. B. Weinmüller, Global Error Estimates for Collocation Applied to BVPs with an Essential Singularity, ANODE 2003 - Auckland Numerical ODEs, Auckland, New Zealand, July 2003. Joint with W. Auzinger, O.Koch.

E. B. Weinmüller, Numerical Solution of Singular Boundary Value Problems in ODEs, Advances in Numerical Algorithms, Graz, Austria, September 2003. Joint with W. Auzinger, O.Koch (invited talk).

H. Hofstätter, Defect Correction for Geometric Integrators, APLIMAT 2004, Bratislava, Slovakia, February 2004. Joint with O. Koch.

E. B. Weinmüller, Generalized Defect Correction for ODEs, ASCOMS '04, Cancun, Mexico, May 2004. Joint with W. Auzinger, H. Hofstätter, O. Koch, W. Kreuzer.

E. B. Weinmüller, From Nonlinear PDEs to Singular ODEs, The Third International Conference on the Numerical Solution of Volterra and Delay Equations, Tempe, Arizona, USA, May 2004. Joint with C.J. Budd, O. Koch.

You can view the abstract of this talk here.

E. B. Weinmüller, Software Development for Singular Boundary Value Problems, CBC Workshop, Györ, Hungary, October 2004. Joint with W. Auzinger, O. Koch, D. Praetorius.

W. Auzinger, Transformed Companion Matrices as a Theoretical Tool in the Numerical Analysis of Differential Equations, CBC Workshop, Györ, Hungary, October 2004. Joint with O. Koch, G. Schranz-Kirlinger.

You can view the abstract of this invited talk here.

E. B. Weinmüller, Adaptive Grid Control for Singular BVPs, Adaptivity and Beyond: Computational Methods for Solving Differential Equations, Vancouver, Canada, August 2005. Joint with W. Auzinger, G. Kitzhofer, O. Koch.

You can view the abstract of this talk here.

W. Auzinger, Präzise und effiziente a posteriori Fehlerschätzung bei impliziten und singulären Randwertproblemen, 16. ÖMG-Kongress, Klagenfurt, Austria, September 2005. Joint with E. Karner, O.Koch, D. Praetorius, E. B. Weinmüller.

You can view the abstract of this talk here.

G. Schranz-Kirlinger, Kanonische Formen für Begleitmatrizen und Anwendungen, 16. ÖMG-Kongress, Klagenfurt, Austria, September 2005. Joint with W. Auzinger, O.Koch.

G. Schranz-Kirlinger, Canonical Forms for Companion Matrices and Applications, SAM Conference, Zurich, October 2005. Joint with W. Auzinger, O.Koch.

E. B. Weinmüller, Collocation Methods for Index-1 DAEs with a Critical Point, Workshop on Differential-Algebraic Equations, Oberwolfach, Germany, April 2006. Joint with O. Koch, R. März, D. Praetorius.

E. B. Weinmüller, Collocation for Index-1 DAEs with a Critical Point, 21st European Conference on Operations Research, Reykjavik, Iceland, July 2006. Joint with O. Koch, R. März, D. Praetorius.

E. B. Weinmüller, Collocation for Index-1 DAEs with a Singularity of the First Kind, SciCADE 2007 --- International Conference on Scientific Computation And Differential Equations, St. Malo, France, July 2007. Joint with O. Koch, R. März, D. Praetorius.

You can view the abstract of this talk here.

A. S. Bagherzadeh, A posteriori Error Estimation for Second Order ODEs via Defect Correction, 5^th Austrian NA Day, Innsbruck, Austria, May 2009. Joint with W. Auzinger and O. Koch.

W. Auzinger, Exact FD Schemes and Defect-Based Error Estimation for Second Order ODEs, Colloquium, Györ University, Györ, Hungary, May 2009. Joint with A. S. Bagherzadeh, and O. Koch.

A. S. Bagherzadeh, Robust and Highly Accurate Error Estimators for Second Order ODEs, 6^th Austrian NA Day, Salzburg, Austria, May 2010. Joint with W. Auzinger and O. Koch.

E. B. Weinmüller, Collocation for Nonlinear Index 1 DAEs with Singular Point, ICIAM 2011, Vancouver, Canada, July 2011. Joint with A. Dick, O. Koch, and R. März.

W. Auzinger, Local Error Estimation for Exponential Splitting Schemes, Conference on Simulation and Optimization, Györ, Hungary, June 2011. Joint with O. Koch and M. Thalhammer.

H. Hofstätter, Convergence Analysis of a Generalized-Laguerre-Fourier-Hermite Method for the Gross-Pitaevskii Equation with Rotation Term, 8^thAustrian Numerical Analysis Day, Vienna, Austria, May 2012. Joint with W. Auzinger, O. Koch, and M. Thalhammer.

H. Hofstätter, Convergence Analysis of a Generalized-Laguerre-Fourier-Hermite Method for the Gross-Pitaevskii Equation with Rotation Term, Workshop on Innovative Time Integration, Innsbruck, Austria, May 2012. Joint with W. Auzinger, O. Koch, and M. Thalhammer.

W. Auzinger, Defect-based error analysis of exponential splitting methods, Conference on Theory of Approximation of Functions and its Applications, Kamieniec Podolski, Ukraine, May/June 2012. Joint with O. Koch and M. Thalhammer.

W. Auzinger, Defect and local error of exponential splitting schemes, The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, USA, July 2012. Joint with O. Koch and M. Thalhammer.

H. Hofstätter, A Perl Program for the Symbolic Manipulation of Flows of Differential Equations and Its Application to the Analysis of Defect-Based Error Estimators for Splitting Methods, 9th Austrian NA Day, Graz, April 2013. Joint with W. Auzinger, O. Koch, and M. Thalhammer.

W. Auzinger, Representation and Estimation of the Local Error of Higher-Order Exponential Splitting Schemes Involving two or three Sub-Operators, 12th International Conference on Numerical Analysis and Applied Mathematics, Rhodes, September 2014. Joint with O. Koch and M. Thalhammer.

W. Auzinger, Representation and Estimation of Local Errors for Splitting Methods Involving two or three Parts, 8th NAI Workshop on Numerical Analysis of Evolution Equations, Innsbruck, October 2014. Joint with H. Hofstätter, O. Koch, and M. Thalhammer.

Th. Kassebacher, Adaptive Time Splitting for Nonlinear Schrödinger Equations in the Semiclassical Regime, 8th NAI Workshop on Numerical Analysis of Evolution Equations, Innsbruck, October 2014. Joint with W. Auzinger, O. Koch, and M. Thalhammer.

W. Auzinger, Representation and estimation of the local error of higher-order exponential splitting schemes involving two or three sub-operators, Mathematical Seminar, University of Tartu, Estonia, September 2014. Joint with O. Koch and M. Thalhammer.

Th. Kassebacher, Adaptive Time Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Regime, 11th Austrian Numerical Analysis Day, Linz, May 2015. Joint with W. Auzinger, O. Koch, and M. Thalhammer.

H. Hofstätter, On Splitting Methods for Nonlinear Parabolic Evolution Equations, 11th Austrian Numerical Analysis Day, Linz, May 2015. Joint with W. Auzinger, O. Koch, and M. Thalhammer.

W. Auzinger, Splitting Methods for Evolution Equations, Local Error Estimation, Adaptivity, International V. Skorobohatko Mathematical Conference, Drohobych, Ukraine, August 2015. Joint with H. Hofstätter, D. Ketcheson, and O. Koch.

W. Auzinger, Splitting schemes, order conditions, and optimized pairs, SciCADE - International Conference on Scientific Computing and Differential Equations 2015, Potsdam, Germany, September 2015. Joint with H. Hofstätter, D. Ketcheson, and O. Koch.

T. Kassebacher, Convergence of adaptive splitting and finite element methods for the Schrödinger-Poisson equation, SciCADE - International Conference on Scientific Computing and Differential Equations 2015, Potsdam, Germany, September 2015. Joint with W. Auzinger, O. Koch, and M. Thalhammer.

H. Hofstätter, Time propagation for Schrödinger-type equations with expensive nonlinearity, Austrian Numerical Analysis Day 2017, Salzburg, May 2017. Joint with O. Koch.

H. Hofstätter, Time propagation for Schrödinger-type equations with expensive nonlinearity, University of Innsbruck, Innsbruck, July 2017. Joint with O. Koch.

S. Donsa, Anderson localization of a one-dimensional Bose-Einstein condensate after long-time expansion, Vienna young Scientists Symposium, Vienna, June 2016. Joint with H. Hofstätter, O. Koch, J. Burgdörfer, and I. Brezinova.

I. Brezinova (invited talk), Expansion of Bose-Einstein condensates in disorder: Anderson localization and wave chaos, International Workshop on Quantum-Classical Transition in Many-Body Systems, Dresden, Germany, February 2017. Joint with S. Donsa, H. Hofstätter, O. Koch, and J. Burgdörfer.

H. Hofstätter, Order conditions for exponential integrators, 14th Austrian Numerical Analysis Day 2018, Klagenfurt, May 2018. Joint with W. Auzinger and O. Koch.

T. Jawecki, A computable strict upper bound for Krylov subspace approximations to the exponential of skew-Hermitian matrices, 14th Austrian Numerical Analysis Day 2018, Klagenfurt, May 2018. Joint with W. Auzinger and O. Koch.

W. Auzinger (invited talk), Sharp a posteriori error estimation for symmetric one-step integrators, International Conference on Modern Problems of Mechanics and Mathematics, Lviv, Ukraine, May 2018. Joint with H. Hofstätter and O. Koch.

W. Auzinger (invited talk), Sharp local error estimation for time-reversible one-step schemes, Workshop `Modern Numerical Methods for Quantum Mechanics II', Gdansk, Poland, June 2018. Joint with H. Hofstätter and O. Koch.

H. Hofstätter, Order conditions for exponential integrators, poster presentation at the Workshop `Modern Numerical Methods for Quantum Mechanics II', Gdansk, Poland, June 2018. Joint with W. Auzinger and O. Koch.

T. Jawecki, A computable strict upper bound for Krylov subspace approximations to the exponential of skew-Hermitian matrices, poster presentation at the Workshop `Modern Numerical Methods for Quantum Mechanics II', Gdansk, Poland, June 2018. Joint with W. Auzinger and O. Koch. Also supported by Doctoral Program TU-D.

You can download this poster as a .pdf file.

W. Auzinger, Adaptive Exponential Integrators for MCTDHF 12th International Conference on Large-Scale Scientific Computations, Sozopol (Bulgaria), 2019. Joint with A. Grosz, H. Hofstätter, 0. Koch:

H. Hofstätter, An algorithm for computing coefficients of words in expressions envolving exponentials and its application to the construction of exponential integrators, 21st International Workshop on Computer Algebra in Scientific Computing, Moskow, Russia, August 2019. Joint with W. Auzinger, 0. Koch.

W. Auzinger. Precise local error control for symmetric one-step schemes applied to nonlinear evolution equations, SciCADE 2019, International Conference on Scientific Computation and Differential Equations, Innsbruck, July 2019. Joint with H. Hofstätter, O. Koch.

T. Jawecki, Computable upper error bounds for Krylov subspace approximations to matrix exponentials, SciCADE 2019, International Conference on Scientific Computation and Differential Equations, Innsbruck, July 2019. Joint with W. Auzinger, and O. Koch.

W. Auzinger, Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime, ParNum 2019, Dubrovnik, Croatia, October 2019. Joint with H. Hofstätter, O. Koch, K. Kropielnicka, and P. Singh.

W. Auzinger, Adaptive Time Propagation of the MCTDHF Equations, 6th Workshop on Stability and Discretization Issues in Differential Equations, Budapest, Hungary, June 2022. Joint with A. Grosz, H. Hofstätter, and O. Koch.

W. Auzinger, Adaptive Exponential Splitting, joint with O. Koch. FAATNA 22 - Functional Analysis, Approximation Theory and Numerical Analysis, Matera, Italy, July 2022.

page written by Othmar Koch. last modification: Mon May 09 11:00 MET 2023