Robust IMEX Schemes for Solving Two-Dimensional Reaction–Diffusion Models

In this paper, numerical simulations of two-dimensional reaction–diffusion (for single and multi-species) models are considered for pattern formation processes. The nature of our problems permits the use of two classical approaches. These semi-linear partial differential equations are split into a linear equation which contains the highly stiff part of the problem, and a nonlinear part that is expected to be varying slowly than the linear part. For the spatial discretization, we introduce higher-order symmetric finite difference scheme, and the resulting ordinary differential equations are then solved with the use of the family of implicit–explicit (IMEX) schemes. Stability properties of these schemes as well as the linear stability analysis of the problems are well presented. Numerical examples and results are also given to illustrate the accuracy and implementation of the methods.