Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian

被引：16

作者：

Fardi, M. ^{[1
]}

Zaky, M. A. ^{[2
]}

Hendy, A. S. ^{[3
,4
]}

机构：

[1] Shahrekord Univ, Fac Math Sci, Dept Appl Math, POB 115, Shahrekord, Iran

[2] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh, Saudi Arabia

[3] Ural Fed Univ, Inst Nat Sci & Math, Dept Computat Math & Comp Sci, 19 Mira St, Ekaterinburg 620002, Russia

[4] Benha Univ, Fac Sci, Dept Math, Banha 13511, Egypt

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2023年 / 206卷

关键词：

Multi-term fractional derivative; Distributed fractional derivative; Fractional Laplacian; Non-uniform mesh; Convergence and stability estimates; NUMERICAL APPROXIMATION; CONVOLUTION QUADRATURE; DIFFUSION-EQUATIONS; ERROR ESTIMATE;

D O I：

10.1016/j.matcom.2022.12.009

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, the multi-term temporal fractional order and temporal distributed-order parabolic equations with fractional Laplacian are numerically investigated. Several unconditional stable difference schemes based on non-uniform meshes for solving these differential equations are provided. We find that the constructed nonuniform difference schemes are convergent and it has been shown that the temporal convergence rate is faster and more accurate compared to the uniform difference schemes in case of nonsmooth solutions with respect to time. Some numerical examples are given to verify the theoretical findings. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：614 / 635

页数：22

共 50 条

[41] Finite difference scheme for multi-term variable-order fractional diffusion equation
Xu, Tao
Lu, Shujuan
Chen, Wenping
Chen, Hu
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[42] Finite difference scheme for multi-term variable-order fractional diffusion equation
Tao Xu
Shujuan Lü
Wenping Chen
Hu Chen
Advances in Difference Equations, 2018
[43] Numerical approximation of 2D multi-term time and space fractional Bloch–Torrey equations involving the fractional Laplacian
Xu, Tao
Liu, Fawang
Lü, Shujuan
Anh, Vo V.
Liu, Fawang (f.liu@qut.edu.au), 1600, Elsevier B.V. (393):
[44] WELL-POSEDNESS OF ABSTRACT DISTRIBUTED-ORDER FRACTIONAL DIFFUSION EQUATIONS
Jia, Junxiong
Peng, Jigen
Li, Kexue
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (02) : 605 - 621
[45] AN IMPROVED COLLOCATION TECHNIQUE FOR DISTRIBUTED-ORDER FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
Abdelkawy, M. A.
ROMANIAN REPORTS IN PHYSICS, 2020, 72 (01)
[46] An Efficient Method for Numerical Solutions of Distributed-Order Fractional Differential Equations
Jibenja, N.
Yuttanan, B.
Razzaghi, M.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2018, 13 (11):
[47] A numerical-analytical solution of multi-term fractional-order differential equations
Kukla, Stanislaw
Siedlecka, Urszula
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (07) : 4883 - 4894
[48] Temporal second-order difference methods for solving multi-term time fractional mixed diffusion and wave equations
Du, Rui-lian
Sun, Zhi-zhong
NUMERICAL ALGORITHMS, 2021, 88 (01) : 191 - 226
[49] Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives
Kim, Myong-Ha
Ri, Guk-Chol
Hyong-Chol, O.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2014, 17 (01) : 79 - 95
[50] Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations
Ford, Neville J.
Connolly, Joseph A.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 229 (02) : 382 - 391

← 1 2 3 4 5 →