Numerical solution of Fisher's equation using a moving mesh method
type: Item
instance of: scholarly article
title: Numerical solution of Fisher's equation using a moving mesh method
zbMATH Open document ID: 0927.65108
author: K. Appert
published in: Journal of Computational Physics
publication date: 1999-01-17T00:00:00Z
review text: As it is well-known, \textit{R. A. Fisher} [The wave of advance of advantageous genes. Ann. Eugenics 7, 355 (1937)] introduced a nonlinear parabolic partial differential equation on an initial spating domain to model the simultaneous growth and spread of a dominant gene. In this paper, the two objectives are discussed. The first is to investigate the viability of moving mesh finite difference methods for the approximate solution of the challenging problem. The second objective is to make comparison between the moving mesh partial differential equation method proposed by \textit{W. Huang}, \textit{Y. Ren} and \textit{R. D. Russel} [SIAM J. Numer. Anal. 31, No. 3, 709-730 (1994; Zbl 0806.65092)] and the moving mesh differential-algebraic equation method proposed by \textit{L. S. Mulholland}, \textit{Y. Qiu} and \textit{D. M. Sloan} [J. Comput. Phys. 131, No. 2, 280-298 (1997; Zbl 0868.65057)].
reviewed by: V. V. Strygin
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1240706
zbMATH Keywords: Fisher's equation
zbMATH Keywords: moving mesh method
zbMATH Keywords: travelling wave solutions
zbMATH Keywords: simultaneous growth and spread of a dominant gene
zbMATH Keywords: moving mesh finite difference methods
describes a project that uses: DASSL
MaRDI profile type: Publication
full work available at URL: jcph.1998.6081
OpenAlex ID: W2022169321
DOI: 10.1006/JCPH.1998.6081
description: scientific article; zbMATH DE number 1240706