MATLAB code BVPSUITE for boundary value problems
This MATLAB code provides a GUI for accessing the functionality of a solver for singular or regular boundary value problems in ODEs. The solver can cope with arbitrary order systems of ODEs and DAEs, with multi-point boundary conditions, parameter-dependent and eigenvalue problems, and is equipped with reliable error control and efficient adaptive hesh adaptation. The code is freely available together with comprehensive documentation and relevant publications here.

MATLAB code SBVP for boundary value problems
As a result of our research efforts, a MATLAB 6.0 code for the solution of singular boundary value problems was implemented. The general purpose code SBVP 1.0 can also be used successfully to solve regular problems. Recently, we updated the package to comply with new MATLAB 6.5 standards and corrected some minor bugs and inconveniences. The new package can be downloaded here, and a technical documentation can be found here. For papers referring to the performance of the code and theoretical considerations about the implemented solution method, see the following papers:

• 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, 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, 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, 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.

FORTRAN 90 code for avalanche dynamics
For the computation of the run-up or run-out of dry-flowing avalanches, we implemented a FORTRAN 90 code, based on a solver for singular initial value problems designed earlier by Peter Kofler. The underlying model is due to McClung, see below. The package can be downloaded here. Usage is transparent from the documentation. Descriptions of the model, our code and its performance, and the underlying numerical method are given in the following papers:

• D.M. McClung, A.I. Mears, Dry-flowing avalanche run-up and run-out, J. Glaciol. 41(1995), pp. 359-369.
  
  
  
• 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, 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.
  
  
  
• O. Koch, E. B. Weinmüller, Analytical and Numerical Treatment of a Singular Initial Value Problem in Avalanche Modeling, Appl. Math. Comput. 148(2003), pp. 561-570.
  
  You can view the abstract of this paper or download the entire text as a .pdf file.
  

  page written by Othmar Koch. last modification: Mon Sep 29 16:00 MET 2003