The computation of eigenvalues
of the regular Sturm-Liouville problem
, with periodic
boundary conditions using finite difference and finite element methods is considered. The reduction of the error of the eigenvalues by a simple step-dependent linear multistep method is studied. The classical finite difference method introduced by A. I. Andrew
[BIT 28, No. 2, 254-269 (1988; Zbl 0646.65070
)] is commented. Numerical experiments taking
in the above problem are carried out and the results are tabulated. The usefulness of the approach is shown even for low-lying eigenvalues.