A modified difference scheme for periodic and semiperiodic Sturm-Liouville problems Original Research Article

Computation of eigenvalues of regular Sturm-Liouville problems with periodic and semiperiodic boundary conditions is considered. It is shown that a simple step-dependent linear multistep method can be used to reduce the error of the eigenvalues. By an appropriate minimization of the local error of the method one can obtain even more accurate results. Numerical examples demonstrate the usefulness of the present approach even for low-lying eigenvalues.