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

Iranian Journal of Numerical Analysis and Optimization

مقاله 10، دوره 14، Issue 4 - شماره پیاپی 31، اسفند 2024، صفحه 1247-1279   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.88781.1472

نویسندگان

N.A. Endrie^{* 1}؛ G.F. 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 fractionalorder 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 ε are explored.

کلیدواژه‌ها

Caputo–Fabrizio derivative operator؛ midpoint upwind scheme؛ fractional-order differential equation؛ delay differential equation؛ singularly perturbed problem

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