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Perturbative Linearization of Reaction-Diffusion Equations

Sanjay Puri·Kay Joerg Wiese
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Abstract

We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction-diffusion systems, viz., the Fisher equation and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of our expansion is the corresponding singular-perturbation solution. This approach transforms the solution of nonlinear reaction-diffusion equations into the solution of a hierarchy of linear equations. Our numerical results demonstrate that this hierarchy rapidly converges to the exact solution.

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Sanjay Puri, Kay Joerg Wiese. 2002-09-23. Perturbative Linearization of Reaction-Diffusion Equations. https://doi.org/10.1088/0305-4470%2F36%2F8%2F303

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