Uniformly convergent numerical solution for caputo fractional order singularly perturbed delay differential equation using extended cubic B-spline collocation scheme

Iranian Journal of Numerical Analysis and Optimization

مقاله 6، دوره 14، Issue 3 - شماره پیاپی 30، آذر 2024، صفحه 762-795   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.86894.1393

نویسندگان

N.A. Endrie^{* 1}؛ G.F. Duressa²

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 article presents a parameter uniform convergence numerical scheme for solving time fractional order singularly perturbed parabolic convection-diffusion differential equations with a delay. We give a priori bounds on the exact solution and its derivatives obtained through the problem’s asymp-totic analysis. The Euler’s method on a uniform mesh in the time direction and the extended cubic B-spline method with a fitted operator on a uniform mesh in the spatial direction is used to discretize the problem. The fitting factor is introduced for the term containing the singular perturbation pa-rameter, and it is obtained from the zeroth-order asymptotic expansion of the exact solution. The ordinary B-splines are extended into the extended B-splines. Utilizing the optimization technique, the value of μ (free param-eter, when the free parameter μ tends to zero the extended cubic B-spline reduced to convectional cubic B-spline functions) is determined. It is also demonstrated that this method is better than some existing methods in the literature.

کلیدواژه‌ها

Singularly perturbed problem؛ Fractional derivative؛ Artificial viscosity؛ Delay differential equation

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