Pointwise error estimates for a system of two singularly perturbed time‐dependent semilinear reaction–diffusion equations

Abstract

We present a finite difference method for a system of two singularly perturbed initial‐boundary value semilinear reaction–diffusion equations. The highest order derivatives are multiplied by small perturbation parameters of different magnitudes. The problem is discretized using a central difference scheme in space and backward difference scheme in time on a Shishkin mesh. The convergence analysis has been given, and it has been established that the method enjoys almost second‐order parameter‐uniform convergence in space and first‐order in time. Numerical experiments are conducted to demonstrate the efficiency of the method.