The Numerical Methods of Eigenvalues and Eigenfunctions of Perturbed Self-Adjoin Operator Finding

S. I. Kadchenko   ; S. N. Kakushkin

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 13 (2012), pp. 45-57

Résumé

In work are received simple formulas of the calculation eigenvalues and analytical formulas of finding «weighed» corrections of the perturbation theory of the discrete semi bounded from below operators. Estimations remainder of the sum of the Reley-Shredinger's functional series are received also. On the base of received formulas was created non-iteration numerical method, which allowed to find the eigenvalues and meanings of eigenfunctions perturbed spectral problem. The numerical experiment for finding of the eigenfeatures by the Laplas's operator, which was perturbed by operator of the multiplying on twice continuously differentiated function, was organized. From the experiment seen, that results numerical accounts of eigenvalues and meanings of eigenfunctions well-agree with result, which received by well-known methods: finding eigenvalues were compared with method Leverrie, and meanings of eigenfunctions — with methods by Danilevskiy A. M. and Krylov A. N.

Détail

Keywords: eigenvalues, eigenfunctions, «weighted» corrections of the perturbation theory, perturbed operators.

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