On the eigenvalue problem − y ″ + f ( x ) y = λ y on a semi infinite interval

In this paper, we are concerned with the solution of a class of boundary value problems − y ″ + f ( x ) y = λ y , 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...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical and computer modelling 2007-08, Vol.46 (3), p.316-330
Main Authors: Leung, Issic Kui Chiu, Shivakumar, P.N.
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
Differential equations
Eigenvalues
Exact sciences and technology
Infinite matrices
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Semi infinite interval
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we are concerned with the solution of a class of boundary value problems − y ″ + f ( x ) y = λ y , 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 | y i v ( x ) | is bounded. The theory is applied to compute the eigenvalues when f ( x ) = x 2 for which explicit solutions are known.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2006.09.017