A symbolic-numerical algorithm for the computation of matrix elements in the parametric eigenvalue problem

A symbolic-numerical algorithm for the computation of the matrix elements in the parametric eigenvalue problem to a prescribed accuracy is presented. A procedure for calculating the oblate angular spheroidal functions that depend on a parameter is discussed. This procedure also yields the correspond...

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Bibliographic Details
Published in:Programming and computer software Vol. 33; no. 2; pp. 105 - 116
Main Authors: Vinitsky, S. I., Gerdt, V. P., Gusev, A. A., Kaschiev, M. S., Rostovtsev, V. A., Samoilov, V. N., Tyupikova, T. V., Chuluunbaatar, O.
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.03.2007
Subjects:
Algorithms
Asymptotic series
Boundary value problems
Eigenvalues
Eigenvectors
Kantorovich method
Numerical analysis
Parameters
Partial differential equations
ISSN:0361-7688, 1608-3261
Online Access:Get full text
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Summary:A symbolic-numerical algorithm for the computation of the matrix elements in the parametric eigenvalue problem to a prescribed accuracy is presented. A procedure for calculating the oblate angular spheroidal functions that depend on a parameter is discussed. This procedure also yields the corresponding eigenvalues and the matrix elements (integrals of the eigenfunctions multiplied by their derivatives with respect to the parameter). The efficiency of the algorithm is confirmed by the computation of the eigenvalues, eigenfunctions, and the matrix elements and by the comparison with the known data and the asymptotic expansions for small and large values of the parameter. The algorithm is implemented as a package of programs in Maple-Fortran and is used for the reduction of a singular two-dimensional boundary value problem for the elliptic second-order partial differential equation to a regular boundary value problem for a system of second-order ordinary differential equations using the Kantorovich method.
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ISSN:0361-7688
1608-3261
DOI:10.1134/S0361768807020089