A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay

Document Type : Research Article

Author

Department of Mathematics, Wollega University, Nekemte, Ethiopia

Abstract

This paper presents a parameter-uniform numerical scheme for the solution of two-parameter singularly perturbed parabolic convection-diffusion problems with a delay in time. The continuous problem is semi-discretized using the Crank-Nicolson finite difference method in the temporal direction. The resulting differential equation is then discretized on a uniform mesh using the fitted operator finite difference method of line scheme. The method is shown to be accurate in O((Δt)2+N−2), where N is the number of mesh points in spatial discretization and Δt is the mesh length in temporal discretization. The parameter-uniform convergence of the method is shown by establishing the theoretical error bounds. Finally, the numerical results of the test problems validate the theoretical error bounds.

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Journal of Mathematical Modeling
Volume 11, Issue 2
July 2023
Pages 395-410

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