A linearly implicit predictor-corrector method for reaction-diffusion equations

Abstract

A novel linearly implicit predictor-corrector scheme is developed for the numerical solution of reaction-diffusion equations. Iterative processes are avoided by treating the nonlinear reaction terms explicitly, while maintaining superior accuracy and stability properties compared to the well-known θ methods and linearly implicit Runge-Kutta methods. The proposed method allows the opportunity of solving large systems of reaction-diffusion equations by alleviating the necessity of solving the accompanying large linear systems of algebraic equations due to the natural parallelism which surfaces across the system. Numerical results confirm the enhanced stability, accuracy and efficiency of the method when applied to reaction-diffusion equations arising in biochemistry and population ecology.