Some new finite difference methods for computing eigenvalues of two-point boundary-value problems
type: Item
instance of: scholarly article
title: Some new finite difference methods for computing eigenvalues of two-point boundary-value problems
zbMATH Open document ID: 0608.65051
DOI: 10.1016/0898-1221(85)90093-8
author: Riaz A. Usmani
publication date: 1985-01-01T00:00:00Z
review text: The second order homogeneous linear differential equation \(y''+\{\lambda q(x)-p(x)\}y=0\) with the homogeneous boundary conditions \(\alpha y'(a)+\beta y(a)=0\) and \(\gamma y'(b)+\delta y(b)=0\) is considered. Under natural assumptions for p(x) and q(x) of this eigenvalue problem, some finite difference schemes of fourth and sixth order are derived to have band-structured coefficient matrices. The convergence of the schemes with respect to the discretization step-size h is shown to be quadratic or cubic in each case. Three numerical examples are given to illustrate the convergence.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 3984489
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: finite difference schemes
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
reviewed by: Taketomo Mitsui
MaRDI profile type: Publication
full work available at URL: 0898-1221(85)90093-8
OpenAlex ID: W2051328049
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cites work: Boundary Value Techniques for the Numerical Solution of Certain Initial Value Problems in Ordinary Differential Equations
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published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 3984489