On the eigenvalue problem -y"+ f(x)y=λy on a semi infinite interval

Kui Chiu Issic LEUNG, P. N. SHIVAKUMAR

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Abstract

In this paper, we are concerned with the solution of a class of boundary value problems −y″+f(x)y=λy, y(0)=0, y(∞)=0, where f(x) monotonically increases to infinity as n increases to infinity. We use finite difference scheme to reduce the system to an equivalent system of an infinite linear algebraic eigenvalue problem. We give a precise error analysis for the eigenvalues of the approximate system and an error analysis for the continuous system under the condition that |yⁱ ̌(x)| is bounded. The theory is applied to compute the eigenvalues when f(x)=x² for which explicit solutions are known. Copyright © 2007 Elsevier.
Original languageEnglish
Pages (from-to)316-330
JournalMathematical and Computer Modelling
Volume46
Issue number3/4
DOIs
Publication statusPublished - Aug 2007

Citation

Leung, I. K. C., & Shivakumar, P. N. (2007). On the eigenvalue problem -y"+ f(x)y=λy on a semi infinite interval. Mathematical and Computer Modelling, 46(3/4), 316-330.

Keywords

  • Differential equations
  • Semi infinite interval
  • Eigenvalues
  • Infinite matrices

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