Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations

Abstract. We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polyno-mial 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 eigenfunc-tions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim. 1