TY - JOUR
T1 - Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 439
EP - 454
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.031116.080317a
UR - https://global-sci.org/intro/article_detail/eajam/10758.html
KW - Fractional sub-diffusion equation, unbounded domain, local artificial boundary conditions, finite difference method, Caputo time-fractional derivative.
AB - <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>