Perturbative Linearization of Reaction-Diffusion Equations
Condensed Matter
2009-11-07 v1
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.
Cite
@article{arxiv.cond-mat/0209524,
title = {Perturbative Linearization of Reaction-Diffusion Equations},
author = {Sanjay Puri and Kay Joerg Wiese},
journal= {arXiv preprint arXiv:cond-mat/0209524},
year = {2009}
}
Comments
13 pages, 4 figures, latex2e