Coupled systems of reaction-diffusion equations are usually solved using a unified time step determined by the most restrictive time scale in the system. We demonstrate in this paper that this time step could be excessively small in many situations, and discuss a more efficient time integration method that does not require linearization procedure and uses different time steps for different equations in a coupled system, depending on their respective time scales. The basic idea is to decouple the system of equations and then apply different time steps to different equations with various time scales. This will also eliminate the need for linearization. Numerical results from a test problem will be discussed to demonstrate significant improvement in computational efficiency.
An Efficient Computational Method for Simulations of Reaction-Diffusion ProcessesComputer Physics Communication
Citation InformationCao, L., Zhu, J., and Cinnella, P. (2000). An Efficient Computational Method for Simulations of Reaction-diffusion Processes. Computer Physics Communication, 126(1-2), 41 - 46, doi: 10.1016/S0010-4655(99)00226-X.