Effective solution to the Sturm-Liouville problem. (English. Russian original) Zbl 0887.65090

Nesterov, S. V.; Akulenko, L. D.

Phys.-Dokl. 41, No. 3, 112-114 (1996); translation from Dokl. Akad. Nauk 347, No. 1, 44-46 (1996).

A new numerical analytical method for solving the Sturm-Liouville problem is developed. Two-sided estimates of the first eigenvalue are constructed. An original determination, not encountered in mathematical literature, for a small parameter of the problem is given. A bound refinement procedure for the eigenvalues and eigenfunctions obtained by the Rayleigh-Ritz method is constructed. A stable calculation method is developed that has an improved convergence and is quite suitable for implementation by modern computing tools. Calculation results for several model examples confirm the significant advantages of the suggested method, i.e., its simplicity, compactness, and convergence rate as compared to the known approaches.

MSC:

65L15	Numerical solution of eigenvalue problems involving ordinary differential equations
34L15	Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators

Keywords:

two-sided estimates; numerical analytical method; Sturm-Liouville problem; eigenvalue; eigenfunctions; Rayleigh-Ritz method; convergence