Compact implicit difference approximation for time-fractional diffusion-wave equation

被引：29

作者：

Ali, Umair ^{[1
]}

Iqbal, Azhar ^{[2
]}

Sohail, Muhammad ^{[1
]}

Abdullah, Farah Aini ^{[3
]}

Khan, Zohaib ^{[4
,5
]}

机构：

[1] Inst Space Technol, Dept Appl Math & Stat, Islamabad 44000, Pakistan

[2] Prince Mohammad Bin Fahd Univ, Math & Nat Sci, Al Khobar 31952, Saudi Arabia

[3] Univ Sains Malaysia, Sch Math Sci, George Town 11800, Malaysia

[4] Univ Tun Hussein Onn Malaysia, Fac Mech & Mfg Engn, Batu Pahat 86400, Johor, Malaysia

[5] Quaid E Awam Univ Engn Sci & Technol Larkana, Dept Mech Engn, Sindh, Pakistan

来源：

ALEXANDRIA ENGINEERING JOURNAL | 2022年 / 61卷 / 05期

关键词：

Compact approximation; Implicit difference scheme; Fractional diffusion-wave equation; Grtinwald Letnikov formula; Stability; Consistency; Convergence; SCHEME; HEAT;

D O I：

10.1016/j.aej.2021.09.005

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this article, developed the compact implicit difference method based Grunwald Letnikov formula (GLF) to compute the solution of the time-fractional diffusion-wave equation (TFDWE) describing wave propagation phenomenan having order alpha (1 < alpha < 2). The fractional derivative is in Caputo sense. The theoretical analysis such as stability, consistency, convergence and solvability of the said scheme are discussed and proved that the scheme is conditionally stable and convergent with the order (tau(2) (Delta x)(4)). The numerical results compared with the recent existed method. The results of the numerical examples show that the GLF and the proposed method is very accurate and efficient for time fractional diffusion-wave equation. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.

引用

页码：4119 / 4126

页数：8

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