@Article{EAJAM-7-439,
author = {Hongwei Li, Xiaonan Wu and Jiwei Zhang},
title = {Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {7},
number = {3},
pages = {439--454},
abstract = {<p style="text-align: justify;">The numerical solution of the time-fractional sub-diffusion equation on an
unbounded domain in two-dimensional space is considered, where a circular artificial
boundary is introduced to divide the unbounded domain into a bounded computational
domain and an unbounded exterior domain. The local artificial boundary conditions for
the fractional sub-diffusion equation are designed on the circular artificial boundary by
a joint Laplace transform and Fourier series expansion, and some auxiliary variables are
introduced to circumvent high-order derivatives in the artificial boundary conditions.
The original problem defined on the unbounded domain is thus reduced to an initial
boundary value problem on a bounded computational domain. A finite difference and
L1 approximation are applied for the space variables and the Caputo time-fractional
derivative, respectively. Two numerical examples demonstrate the performance of the
proposed method.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.031116.080317a},
url = {http://global-sci.org/intro/article_detail/eajam/10758.html}
}