We demonstrate that eigenvalue problems in ordinary differential equations can be
recast in a formulation suitable for the solution by polynomial collocation. It is
shown that the well-posedness of the two formulations is equivalent in the regular as
well as in the singular case. Thus, a collocation code equipped with asymptotically
correct error estimation and adaptive mesh selection can be successfully applied
to compute the eigenvalues and eigenfunctions efficiently and with reliable
control of the accuracy. Numerical examples illustrate this claim.