Obtaining artificial boundary conditions for fractional sub-diffusion equation on space two-dimensional unbounded domains

被引：13

作者：

Ghaffari, Rezvan ^{[1
]}

Hosseini, S. Mohammad ^{[1
]}

机构：

[1] Tarbiat Modares Univ, Fac Math Sci, Dept Appl Math, Tehran, Iran

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 68卷 / 1-2期

关键词：

Fractional sub-diffusion equation; Artificial boundary condition; Two-dimensional unbounded domain; Laplace transform; Modified Bessel equation; FINITE-DIFFERENCE APPROXIMATION; DIRECTION IMPLICIT SCHEMES; HEAT-EQUATION; CONVERGENCE;

D O I：

10.1016/j.camwa.2014.05.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider fractional sub-diffusion equation on two-dimensional unbounded domains and obtain an exact and some approximating artificial boundary conditions for it by a joint application of the Laplace transform and the Fourier series expansion. In order to test the derived artificial boundary condition, after reducing the main problem to an initial-boundary value problem on bounded domain by imposing the obtained boundary condition, we just use classical Crank-Nicolson method for space variables and L1 approximation for the fractional time derivative. Some numerical examples are given which confirm the effectiveness of the proposed artificial boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：13 / 26

页数：14

共 50 条

[31] Two-dimensional nonlinear time fractional reaction-diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media
Pandey, P.
Das, S.
Craciun, E-M.
Sadowski, T.
[J]. MECCANICA, 2021, 56 (01) : 99 - 115
[32] A numerical treatment of the two-dimensional multi-term time-fractional mixed sub-diffusion and diffusion-wave equation
Ezz-Eldien, S. S.
Doha, E. H.
Wang, Y.
Cai, W.
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 91
[33] HELMHOLTZ EQUATION WITH ARTIFICIAL BOUNDARY CONDITIONS IN A TWO-DIMENSIONAL WAVEGUIDE
Mitsoudis, D. A.
Makridakis, Ch
Plexousakis, M.
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 44 (06) : 4320 - 4344
[34] A Fast Temporal Second Order Difference Scheme for the Fractional Sub-diffusion Equations on One Dimensional Space Unbounded Domain
Qi, Ren-Jun
Sun, Zhi-Zhong
[J]. JOURNAL OF MATHEMATICAL STUDY, 2023, 56 (02) : 173 - 205
[35] Numerical inversions for diffusion coefficients in two-dimensional space fractional diffusion equation
Chi, Guangsheng
Li, Gongsheng
[J]. INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2018, 26 (07) : 996 - 1018
[36] A fourth-order compact solution of the two-dimensional modified anomalous fractional sub-diffusion equation with a nonlinear source term
Abbaszadeh, Mostafa
Mohebbi, Akbar
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (08) : 1345 - 1359
[37] Solution of two-dimensional modified anomalous fractional sub-diffusion equation via radial basis functions (RBF) meshless method
Mohebbi, Akbar
Abbaszadeh, Mostafa
Dehghan, Mehdi
[J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2014, 38 : 72 - 82
[38] The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains
Yu, Hao
Wu, Boying
Zhang, Dazhi
[J]. NUMERICAL ALGORITHMS, 2019, 82 (04) : 1221 - 1250
[39] The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains
Hao Yu
Boying Wu
Dazhi Zhang
[J]. Numerical Algorithms, 2019, 82 : 1221 - 1250
[40] NUMERICAL SIMULATIONS FOR THE VARIABLE ORDER TWO-DIMENSIONAL REACTION SUB-DIFFUSION EQUATION: LINEAR AND NONLINEAR
Adel, Mohamed
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (01)

← 1 2 3 4 5 →