An efficient high-order algorithm for solving systems of reaction-diffusion equations

An efficient higher-order finite difference algorithm is presented in this article for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Pade approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm. (C) 2002 Wiley Periodicals, Inc.