A novel mid-point upwind scheme for fractional order singularly perturbed convection-diffusion delay differential equation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 مرداد 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.88781.1472

نویسندگان

Nuru Ahmed Endrie^{* 1}؛ Gemechis File Duressa^{1، 2}

¹Department of Mathematics, College of Natural and Computational Science, Arba Minch University, Arba Minch, Ethiopia.

²Department of Mathematics, College of Natural and Computational Science, Jimma University, Jimma, Ethiopia.

چکیده

This study presents a numerical approach for solving temporal fractional order singularly perturbed parabolic convection-diffusion differential equations with a delay using a uniformly convergent scheme. We use the asymptotic analysis of the problem to offer a priori bounds on the exact solution and its derivatives. To discretize the problem, we use the implicit Euler technique on a uniform mesh in time and the midpoint upwind finite difference approach on a piece-wise uniform mesh in space. The proposed technique has a nearly first-order uniform convergence order in both spatial and temporal dimensions. To validate the theoretical analysis of the scheme, two numerical test situations for various values of $\epsilon$ are explored.

کلیدواژه‌ها

Caputo Fabrizio derivative operator؛ Midpoint upwind scheme؛ Fractional order differential equation؛ Delay differential equation؛ Singularly perturbed problem