An efficient parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation

被引：3
作者：
Alavi, Javad [1 ]
Aminikhah, Hossein [1 ,2 ]
机构：
[1] Univ Guilan, Fac Math Sci, Dept Appl Math & Comp Sci, POB 1914, Rasht 41938, Iran
[2] Univ Guilan, Ctr Excellence Math Modelling Optimizat & Combinat, POB 1914, Rasht 41938, Iran
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2023年 / 42卷 / 08期
关键词：
Parametric finite difference method; Orthogonal spline approximation; Nonlinear time-fractional partial integro-differential equation; Caputo fractional derivative; Rieman-Liouville fractional integral; Weakly singular kernel; SCHEME; DIFFUSION; TRANSFORM; SPACE;
D O I：
10.1007/s40314-023-02491-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a numerical method is presented to solve a nonlinear weakly singular time-fractional partial integro-differential equation with Caputo fractional derivative. An orthogonal basis of spline space called O-spline is introduced, which is used for spatial approximations. Also, an approximation for the temporal Riemann-Liouville integral of the function is presented. A new parametric approximation is developed for the temporal Caputo fractional derivative of the function. Finally, using the weighted finite difference method, a numerical time scheme is obtained to approximate the equation. The convergence of this numerical scheme is investigated and some numerical examples are provided to illustrate the accuracy and efficiency of the method.
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页数：25
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