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

Iranian Journal of Numerical Analysis and Optimization

مقاله 10، دوره 15، Issue 1 - شماره پیاپی 32، خرداد 2025، صفحه 255-283   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.89176.1490

نویسندگان

W.S. Hailu^{* 1}؛ G.F. Duressa²

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

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

چکیده

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.

کلیدواژه‌ها

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

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