Functional -discrete method (FD-method) for matrix Sturm-Liouville problems I

by    B. I. Bandyrskii

Preprint series: 05-03, Reports on Numerical Mathematics

B. I. Bandyrskii

65L15 Eigenvalue problems
65Y20 Complexity and performance of numerical algorithms [See also 68Q25]
34D10 Perturbations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions

Abstract: A new algorithm for Sturm-Liouville problems with matrix coefficients is proposed which possesses the convergence rate of a geometric progression with a denominator depending inversely proportional from the order numbe of an eigenvalue. The asymptotical behavior of the distance between neighboring eigenvalues is investigated in the case when the order number tends to infinity. Numerical examples are given.

Keywords: Sturm-Liouville problem with matrix coefficients, asymptotic expansions, apriori estimates

Upload: 2005-03-30

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