Layer-resolving mesh method for convection-diffusion delay problems with boundary turning points

Document Type : Research Article

Authors

Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia.

Abstract

This paper introduces a numerical scheme designed to solve time-delay singularly perturbed parabolic convection-diffusion problems with turning points. A small parameter induces boundary layers, making standard methods ineffective. To tackle these challenges, we developed a layer-resolving numerical scheme using the Crank-Nicolson method (time) and a central finite difference method on a Shishkin mesh (space). The stability and parameter-uniform convergence analysis show that the error decreases quadratically. Numerical results demonstrate higher accuracy than existing approaches.

Keywords

Main Subjects


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