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

Nana A. Mbroh and Justin B. Munyakazi

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 165, issue C, 156-171

Abstract: 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.

Keywords: Parabolic convection–diffusion problems; Singular perturbations; Fitted operator finite difference methods; Convergence analysis; Method of lines (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:165:y:2019:i:c:p:156-171

DOI: 10.1016/j.matcom.2019.03.007

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