Solving reaction-diffusion and advection problems with Richardson extrapolation

Abstract

Richardson extrapolation is a simple but powerful computational tool to enhance the accuracy of time integration methods. In the past years a few theoretical and partly practical works have been presented on this method. Detailed numerical applications of this method, however, are rarely found in the literature. Therefore, it is worth investigating whether this promising technique lives up to the expectations also in practice. In this paper we investigate the efficiency of the Richardson method in one-dimensional numerical (reaction-diffusion) problems.