Parameter-uniform numerical treatment of singularly perturbed parabolic delay differential equations with nonlocal boundary conditions

Document Type : Research Article

Authors

• W.S. Hailu ¹
• G.F. Duressa ²

¹ Department of Mathematics, Dilla University, Dilla, Ethiopia.

² Department of Mathematics, Jimma University, Jimma, Ethiopia. Department of Mathematics, Arba Minch University, Arba Minch, Ethiopia.

10.22067/ijnao.2024.89176.1490

Abstract

This paper focuses on solving singularly perturbed parabolic equations of the convection-diffusion type with a large negative spatial shift and an integral boundary condition. A higher-order uniformly convergent numer-ical approach is proposed that uses Crank–Nicolson and a hybrid finite difference approximation on a piece-wise uniform Shishkin mesh. Simp-son’s 1/3 integration rule is used to treat the integral boundary condition. The proposed method has been shown to achieve almost second-order uni-form convergence. The computational results derived from the numerical experiment are consistent with the theoretical estimates. Furthermore, the method produces a more accurate result than certain other methods in the literature.

Keywords

• Singular perturbation
• Convection-Diffusion problem
• Fitted mesh method
• Hybrid finite difference scheme
• Integral constraint

Main Subjects

• Numerical Analysis

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