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Mackenzie, J A and Madzvamuse, A (2009) Analysis of stability and convergence of finite-difference methods for a reaction-diffusion problem on a one-dimensional growing domain. IMA Journal of Numerical Analysis, 31 (1). pp. 212-232. ISSN 0272-4979
Full text not available from this repository.Abstract
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.
| Item Type: | Article |
|---|---|
| Additional Information: | My contribution to this article was 50% |
| Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
| Related URLs: | |
| Depositing User: | Anotida Madzvamuse |
| Date Deposited: | 06 Feb 2012 20:47 |
| Last Modified: | 30 Jul 2013 15:02 |
| URI: | http://sro.sussex.ac.uk/id/eprint/28095 |