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Analysis of stability and convergence of finite-difference methods for a reaction-diffusion problem on a one-dimensional growing domain

journal contribution
posted on 2023-06-08, 07:47 authored by J A Mackenzie, Anotida MadzvamuseAnotida Madzvamuse
In this paper we consider the stability and convergence of finite-difference discretizations of a reactiondiffusion equation on a one-dimensional domain that is growing in time. We consider discretizations of conservative and nonconservative formulations of the governing equation and highlight the different stability characteristics of each. Although nonconservative formulations are the most popular to date, we find that discretizations of the conservative formulation inherit greater stability properties. Furthermore, we present a novel adaptive time integration scheme based on the well-known method and describe how the parameter should be chosen to ensure unconditional stability, independently of the rate of domain growth. This work is a preliminary step towards an analysis of numerical schemes for the solution of reactiondiffusion systems on growing domains. Such problems arise in many practical areas including biological pattern formation and tumour growth.

History

Publication status

  • Published

Journal

IMA Journal of Numerical Analysis

ISSN

0272-4979

Publisher

Oxford University Press

Issue

1

Volume

31

Page range

212-232

Department affiliated with

  • Mathematics Publications

Notes

My contribution to this article was 50%

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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