An Efficient High Order Algorithm for Solving Reaction-Diffusion Equations

An efficient higher order finite difference algorithm is presented in this paper for solving systems of two-dimensional reaction-diffusion equations with nonlinear reaction terms. It is fourth order accurate in both the temporal and spatial dimensions. A regular five-point difference of stencil similar to that used in the Crank-Nicolson algorithm, which is only second order accurate in the temporal and spatial dimensions, is used in the discretization. The higher order accuracy in the new algorithm is achieved by using the Pade approximation for the second order spatial derivatives and extrapolations in the temporal dimension. Numerical examples will be presented in the paper to demonstrate efficiency and accuracy improvement using the new algorithm.