A fitted operator finite difference method of lines for singularly perturbed parabolic convection-diffusion problems

摘要

We propose a uniformly convergent finite difference method to solve singularly perturbed time-dependent convection- diffusion problems in the framework of method of lines. The method uses the fitted operator finite difference method to discretize the spatial derivatives followed by the Crank-Nicolson method for the time derivative. Richardson extrapolation is performed in space to improve the accuracy of the method. We prove that the method is uniformly convergent with respect to the perturbation and the discretization parameters. We present numerical simulations to illustrate and confirm the theoretical results. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.