Perturbative Linearization of Reaction-Diffusion Equations
arXiv:cond-mat/0209524 · doi:10.1088/0305-4470/36/8/303
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.
13 pages, 4 figures, latex2e