A MODIFIED DIFFERENCE SCHEME FOR PERIODIC AND SEMIPERIODIC STURM-LIOUVILLE PROBLEMS

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