Higher-order convergence with fractional-step method for singularly perturbed 2D parabolic convection-diffusion problems on Shishkin mesh

In this article, we propose a second-order uniformly convergent numerical method for a singularly perturbed 2D parabolic convection-diffusion initial-boundary-value problem. First, we use a fractional-step method to discretize the time derivative of the continuous problem on uniform mesh in the temporal direction, which gives a set of two ID problems. Then, we use the classical finite difference scheme to discretize those 1D problems on a special mesh, which results almost first-order convergence, i.e., O(N-1+beta ln N + Delta t). To enhance the order of convergence to O(N-2+beta ln(2)N + Delta t(2)), we use the Richardson extrapolation technique. In support of the theoretical results, numerical experiments are performed by employing the proposed technique. (C) 2017 Elsevier Ltd. All rights reserved.