The generalized quasi-linearization method for reaction diffusion equations on an unbounded domain
type: Item
instance of: scholarly article
title: The generalized quasi-linearization method for reaction diffusion equations on an unbounded domain
zbMATH Open document ID: 0938.35076
author: Liwen Wang
author: Aghalaya S. Vatsala
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-06-27T00:00:00Z
review text: The authors extend the method of generalized quasilinearization to reaction diffusion equations on an unbounded domain. The iterates, which are solutions of linear equations starting from lower and upper solutions, converge uniformly and monotonically to the unique solution of a nonlinear reaction diffusion equation in an unbounded domain. Initially an existence theorem for the linear nonhomogeneous reaction diffusion equation in an unbounded domain has been proved under improved conditions. The quadratic convergence has been proved by using a comparison theorem for reaction diffusion equations with ordinary differential equations. This avoids the computational complexity of the quasilinearization method, since the computation of the Green's function at each stage of the iterates is avoided.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 1346381
zbMATH Keywords: quadratic convergence
zbMATH Keywords: comparison theorem
reviewed by: V. Lakshmikantham
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6495
OpenAlex ID: W1970554385
cites work: Methods of nonlinear analysis. Vol. II
cites work: Positive solutions for nonlinear parabolic second initial boundary value problems
cites work: Q5520962
cites work: Q3807603
cites work: Q5569338
cites work: Q4397695
cites work: Nonlinear elliptic boundary-value problems in unbounded domains
cites work: Parabolic systems in unbounded domains. I: Existence and dynamics
cites work: Parabolic systems in unbounded domains. II: Equations with time delays
cites work: Q4313212
cites work: Q4677300
DOI: 10.1006/JMAA.1999.6495
description: scientific article; zbMATH DE number 1346381