Differential equations with piecewise approximate coefficients: Discrete and continuous estimation for initial and boundary value problems
type: Item
instance of: scholarly article
title: Differential equations with piecewise approximate coefficients: Discrete and continuous estimation for initial and boundary value problems
zbMATH Open document ID: 0763.65053
DOI: 10.1016/0898-1221(92)90005-3
author: S. Namasivayam
author: Mohamed K. El-Daou
author: Eduardo L. Ortiz
publication date: 1993-04-01T00:00:00Z
review text: Given a linear second order differential equation together with initial and boundary conditions which guarantee the existence of a unique solution, the authors study the effect of perturbations of the original coefficients of the differential equation on the solution of the corresponding initial or boundary value problems. As remarked in the paper such a study is interesting not only in perturbation theories but also in the numerical solution of initial and boundary value problems by means of Tau and Galerkin type methods. Since it is common in some numerical methods to replace the coefficients of the differential equation by piecewise continuous approximations defined in a suitable way, a natural question is to bound or estimate the effect of such a replacement of the solution. Here, assuming piecewise approximate coefficients, the authors derive error estimates for both the solution and its derivative of discrete and continuous initial and boundary value problems. Finally, a number of numerical examples to show the quality of the estimates are presented.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 148278
zbMATH Keywords: Tau method
zbMATH Keywords: Galerkin method
zbMATH Keywords: linear second order differential equation
zbMATH Keywords: effect of perturbations
zbMATH Keywords: error estimates
zbMATH Keywords: numerical examples
reviewed by: Manuel Calvo
MaRDI profile type: Publication
full work available at URL: 0898-1221(92)90005-3
OpenAlex ID: W2031092662
cites work: Q3332175
cites work: Numerical solution of Mathieu's equation
cites work: A new method for the solution of the Schrödinger equation
cites work: The Tau Method
cites work: Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation
cites work: Solving Linear Boundary Value Problems by Approximating the Coefficients
cites work: Local Piecewise Polynomial Projection Methods for an O.D.E. Which Give High-Order Convergence at Knots
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 148278