Velocity-induced numerical solutions of reaction-diffusion systems on continuously deforming domains

Madzvamuse, Anotida and Maini, Philip K (2007) Velocity-induced numerical solutions of reaction-diffusion systems on continuously deforming domains. Journal of Computational Physics, 225 (1). pp. 100-119. ISSN 00219991

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Abstract

Reaction-diffusion systems have been widely studied in developmental biology, chemistry and more recently in financial mathematics. Most of these systems comprise nonlinear reaction terms which makes it difficult to find closed form solutions. It therefore becomes convenient to look for numerical solutions: finite difference, finite element, finite volume and spectral methods are typical examples of the numerical methods used. Most of these methods are locally based schemes. We examine the implications of mesh structure on numerically computed solutions of a well-studied reaction-diffusion model system on two-dimensional fixed and growing domains. The incorporation of domain growth creates an additional parameter - the grid-point velocity - and this greatly influences the selection of certain symmetric solutions for the ADI finite difference scheme when a uniform square mesh structure is used. Domain growth coupled with grid-point velocity on a uniform square mesh stabilises certain patterns which are however very sensitive to any kind of perturbation in mesh structure. We compare our results to those obtained by use of finite elements on unstructured triangular elements

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Anotida Madzvamuse
Date Deposited: 06 Feb 2012 21:19
Last Modified: 11 Apr 2012 09:52
URI: http://sro.sussex.ac.uk/id/eprint/30790
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