Wavelet-Galerkin method for the reaction-diffusion equation

A Wavelet-Galerkin method was developed for reaction-diffusion problems.In most such problems,the reaction procedure is much faster than the diffusion procedure and the problems include boundary layers which increase the computational complexity.The usual finite element methods and finite difference methods can not capture the boundary layers exactly with acceptable computational complexity.The self-adapted wavelet method gives high accuracy approximate solutions and reduces the computational complexity from O(e~(-2)) to O1eln1e.Two numerical examples illustrate the efficiency of the method.