Numerical methods for systems of nonlinear parabolic equations with time delays
type: Item
instance of: scholarly article
title: Numerical methods for systems of nonlinear parabolic equations with time delays
zbMATH Open document ID: 0941.65083
author: C. V. Pao
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-07-20T00:00:00Z
review text: Some numerical aspects of a class of coupled nonlinear parabolic systems with time delays are investigated. The system of parabolic equations is discretized by the finite difference method which yields a coupled system of nonlinear algebraic equations. The mathematical analysis of the nonlinear system is carried out by the method of upper and lower solutions and its associated monotone iterations. Three monotone iterative schemes are presented and it is shown that the sequence of iterations from each one of these iterative schemes converges monotonically to a unique solution of the finite difference system. A theoretical comparison result for the various monotone sequences and error estimates for the three iterative schemes are obtained. It is also shown that the finite difference solution converges to the classical solution of the parabolic system as the mesh size decreases to zero.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1398607
zbMATH Keywords: nonlinear parabolic systems
zbMATH Keywords: time delays
zbMATH Keywords: finite difference method
zbMATH Keywords: method of upper and lower solutions
zbMATH Keywords: monotone iterations
zbMATH Keywords: error estimates
reviewed by: Violeta A. Kostova
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6619
OpenAlex ID: W2082375119
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DOI: 10.1006/JMAA.1999.6619
description: scientific article; zbMATH DE number 1398607