فهرست مطالب نویسنده:
n.a. endrie
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Iranian Journal of Numerical Analysis and Optimization, Volume:14 Issue: 4, Autumn 2024, PP 1247 -1279This 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.Keywords: Caputo–Fabrizio Derivative Operator, Midpoint Upwind Scheme, Fractional-Order Differential Equation, Delay Differential Equation, Singularly Perturbed Problem
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Iranian Journal of Numerical Analysis and Optimization, Volume:14 Issue: 3, Summer 2024, PP 762 -795This 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.Keywords: Singularly Perturbed Problem, Fractional Derivative, Artificial Viscosity, Delay Differential Equation
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