Difference Approximation for 2D Time-Fractional Integro-Differential Equation with Given Initial and Boundary Conditions

被引：0
|
作者：
Zhang, Xindong [1 ]
Luo, Ziyang [2 ]
Tang, Quan [3 ]
Wei, Leilei [4 ]
Liu, Juan [1 ]
机构：
[1] Guizhou Univ Finance & Econ, Coll Big Data Stat, Guiyang 550025, Peoples R China
[2] Xinjiang Inst Engn, Sch Math & Phys, Urumqi 830023, Peoples R China
[3] Xinjiang Normal Univ, Sch Math Sci, Urumqi 830017, Peoples R China
[4] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Peoples R China
来源：
FRACTAL AND FRACTIONAL | 2024年 / 8卷 / 08期
关键词：
integro-differential equation; Riemann-Liouville derivative; compact finite difference method; stability; convergence; ERROR ANALYSIS; SCHEME; DIFFUSION; ADI; CONDUCTION; SPACE;
D O I：
10.3390/fractalfract8080495
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this investigation, a new algorithm based on the compact difference method is proposed. The purpose of this investigation is to solve the 2D time-fractional integro-differential equation. The Riemann-Liouville derivative was utilized to define the time-fractional derivative. Meanwhile, the weighted and shifted Gr & uuml;nwald difference operator and product trapezoidal formula were utilized to construct a high-order numerical scheme. Also, we analyzed the stability and convergence. The convergence order was O(tau 2+hx4+hy4), where tau is the time step size, hx and hy are the spatial step sizes. Furthermore, several examples were provided to verify the correctness of our theoretical reasoning.
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页数：17
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