A Rayleigh-Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind

Kaya R., TAŞELİ H.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.60, no.6, pp.1107-1129, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1007/s10910-022-01344-9
  • Journal Name: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Chemical Abstracts Core, zbMATH
  • Page Numbers: pp.1107-1129
  • Keywords: Integral equation, Schrodinger equation, Rayleigh-Ritz method Dirichlet boundary value problem, Neumann boundary value problem
  • TED University Affiliated: Yes

Abstract

A Rayleigh-Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrodinger equation -y ''(x) + v(x)y(x) = lambda y(x), x is an element of (-infinity, infinity) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x is an element of [-l, l], where l is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are compared with the very well known eigenvalues of the Schrodinger equation with several types of potential functions v(x). It is shown that the eigenvalues recorded to about 15 significant figures are in excellent agreement with the results that exist in the literature.