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.

引用

页数：17

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