A symbolic-numerical algorithm for the computation of matrix elements in the parametric eigenvalue problem. (English. Russian original) Zbl 1137.65428

Program. Comput. Softw. 33, No. 2, 105-116 (2007); translation from Programmirovanie 33, No. 2, 63-76 (2007).
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.


65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
81V45 Atomic physics
68W30 Symbolic computation and algebraic computation


Full Text: DOI


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