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

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