A discrete Schwarz waveform relaxation method of higher order for singularly perturbed parabolic reaction–diffusion problems

Abstract

We consider singularly perturbed parabolic reaction–diffusion problems of scalar and vector types. We construct a discrete Schwarz waveform relaxation method of higher order for their numerical solution. The method is shown to be parameter-uniformly convergent having almost fourth order in space and first order in time. Further, interesting result proven is much faster convergence of iterative process for small perturbation parameter. Numerical results demonstrating the efficiency of the proposed method and validating the theoretically proven convergence results are given.