A parameter-uniform hybrid finite difference scheme for singularly perturbed system of parabolic convection-diffusion problems

We present the hybrid finite difference scheme for singularly perturbed system of parabolic convection-diffusion problems exhibiting overlapping boundary layers. We discretize the time derivative by the backward-Euler method and the spatial derivatives is discretized by the hybrid difference scheme on Shishkin mesh. We have shown that the presented numerical scheme is parameter-uniform convergent of first-order in temporal variable and almost second-order in spatial variable. Numerical experiments supporting the theoretical results are presented.