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

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.