Description of a Program for Computing Eigenvalues and Eigenfunctions and Their First Derivatives with Respect to the Parameter of the Coupled Parametric Self-Adjoined Elliptic Differential Equations

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  • Authors: Gusev AA1, Chuluunbaatar O2, Vinitsky SI1, Abrashkevich AG3
  • Affiliations:
    1. Joint Institute for Nuclear Research
    2. National University of Mongolia, Mongolia
    3. IBM Toronto Lab
  • Issue: No 2 (2014)
  • Pages: 336-341
  • Section: Articles
  • URL: http://journals.rudn.ru/miph/article/view/8388
  • Cite item

Abstract


Brief description of a FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the coupled parametric self-adjoined elliptic differential equations with the Dirichlet and/or Neumann type boundary conditions on the finite interval. The original problem is projected to the parametric homogeneous and nonhomogeneous 1D boundary-value problems for a set of ordinary second order differential equations which is solved by the finite element method. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Parametric eigenvalues (so-called potential curves) and matrix elements computed by the POTHEA program can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs. As a test desk, the program is applied to the calculation of the potential curves and matrix elements of Schr¨odinger equation for a system of three charged particles with zero total angular momentum.

About the authors

A A Gusev

Joint Institute for Nuclear Research

Email: gooseff@jinr.ru

O Chuluunbaatar

National University of Mongolia, Mongolia

Email: chuka@jinr.ru
School of Mathematics and Computer Science

S I Vinitsky

Joint Institute for Nuclear Research

Email: vinitsky@theor.jinr.ru

A G Abrashkevich

IBM Toronto Lab

Email: aabrashk@ca.ibm.com

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Copyright (c) 2014 Гусев А.А., Чулуунбаатар О., Виницкий С.И., Абрашкевич А.Г.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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