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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 شهریور 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.89176.1490

نویسندگان

Wondimagegnehu Simon Hailu^{* 1}؛ Gemechis File Duressa^{2، 3}

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

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

³Department 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 numerical approach is proposed that uses Crank-Nicolson and a hybrid finite difference approximation on a piece-wise uniform Shishkin mesh. Simpson's 1/3 integration rule is used to treat the integral boundary condition. The proposed method has been shown to achieve almost second-order uniform 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