Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method

Abstract

The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the <italic>regularized sampling method</italic> , an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.