A comparison of two numerical methods for oscillatory reaction-diffusion systems
UNSPECIFIED. (1997) A comparison of two numerical methods for oscillatory reaction-diffusion systems. APPLIED MATHEMATICS LETTERS, 10 (2). pp. 1-5. ISSN 0893-9659Full text not available from this repository.
Reaction-diffusion systems whose kinetics contain a stable limit cycle are an established class of models for a range of oscillatory biological and chemical phenomena. In this paper, the author compares two numerical methods for calculating the oscillatory wake solutions generated by spatially localized perturbations for one particular reaction-diffusion system, of lambda-omega type. The two methods are a semi-implicit, or implicit-explicit, finite difference scheme based on the Crank-Nicolson algorithm, and the method of lines with Gear's method. Though both solutions ultimately converge to a common solution, the approach to this final solution is very different in the two cases. The results provide a clear illustration of the care required in numerical solution of oscillatory reaction-diffusion equations.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||APPLIED MATHEMATICS LETTERS|
|Publisher:||PERGAMON-ELSEVIER SCIENCE LTD|
|Number of Pages:||5|
|Page Range:||pp. 1-5|
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