A compact ADI scheme for two-dimensional fractional sub-diffusion equation with Neumann boundary condition

被引：14

作者：

Cheng, Xiujun ^{[1
,2
]}

Qin, Hongyu ^{[3
]}

Zhang, Jiwei ^{[3
]}

机构：

[1] Zhejiang Sci Tech Univ, Coll Sci, Hangzhou 310018, Peoples R China

[2] Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai 200240, Peoples R China

[3] Wuhan Univ, Sch Math & Stat, Hubei Key Lab Computat Sci, Wuhan 430072, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 156卷

关键词：

Fractional sub-diffusion equation; Neumann boundary conditions; ADI; Convergence; PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT-METHOD; NUMERICAL-SOLUTION; L1-GALERKIN FEMS; ERROR ANALYSIS; FORMULA; MODEL;

D O I：

10.1016/j.apnum.2020.04.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop an effective numerical method for solving the fractional sub-diffusion equation with Neumann boundary conditions. The time fractional derivative is approximated by the L1 scheme on graded meshes, the spatial discretization is done by using the compact finite difference methods. By adding some corrected terms, the fully discrete alternating direction implicit (ADI) method is obtained. Convergence of the scheme is obtained under the assumptions of the weak singularity of solutions. The extension of numerical scheme to the three-dimensional case is presented. Finally, the effectiveness of the proposed method is confirmed by several numerical experiments. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：50 / 62

页数：13

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