Madzvamuse, A. and Maini, P. K. (2007) Velocityinduced numerical solutions of reactiondiffusion systems on continuously growing domains. Journal of Computational Physics, 225 (1). pp. 100119.

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Abstract
Reactiondiffusion 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 wellstudied reactiondiffusion model system on twodimensional fixed and growing domains. The incorporation of domain growth creates an additional parameter – the gridpoint 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 gridpoint 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 

Additional Information:  n/a 
Uncontrolled Keywords:  Reactiondiffusion; Moving grid finite elements; ADI finite difference; Pattern formation; Schnakenberg model; Gridpoint velocity; Growing domain 
Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Centre for Mathematical Biology 
ID Code:  629 
Deposited By:  Philip Maini 
Deposited On:  23 Jul 2007 
Last Modified:  29 May 2015 18:25 
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