A spatial sixth-order numerical scheme for solving fractional partial differential equation

被引：24

作者：

Zhang, Xindong ^{[1
]}

Feng, Yuelong ^{[2
]}

Luo, Ziyang ^{[3
]}

Liu, Juan ^{[1
]}

机构：

[1] Guizhou Univ Finance & Econ, Coll Big Data Stat, Guiyang 550025, Peoples R China

[2] Xinjiang Normal Univ, Sch Math Sci, Urumqi 830017, Xinjiang, Peoples R China

[3] Xinjiang Inst Engn, Sch Math & Phys, Urumqi 830023, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2025年 / 159卷

关键词：

Time-fractional diffusion equation; Caputo-Fabrizio fractional derivative; Finite difference method; Compact difference scheme; DIFFUSION EQUATION; ELEMENT-METHOD;

D O I：

10.1016/j.aml.2024.109265

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a spatial sixth-order numerical scheme for solving the time-fractional diffusion equation (TFDE) is proposed. The convergence order of the constructed numerical scheme is O(tau(2) + h(6)), where tau and h are the temporal and spatial step sizes, respectively. The stability and error estimation of proposed scheme are given by using Fourier method. Some numerical examples are studied to demonstrate the correctness and effectiveness of the scheme and validate the theoretical analysis.

引用

页数：7

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