TY - JOUR
T1 - High-Order Local Artificial Boundary Conditions for the Fractional Diffusion Equation on One-Dimensional Unbounded Domain
AU - Zhang , Wei
AU - Li , Can
AU - Wu , Xiaonan
AU - Zhang , Jiwei
JO - Journal of Mathematical Study
VL - 1
SP - 28
EP - 53
PY - 2017
DA - 2017/03
SN - 50
DO - http://doi.org/10.4208/jms.v50n1.17.03
UR - https://global-sci.org/intro/article_detail/jms/978.html
KW - Fractional subdiffusion equation, high-order absorbing boundary conditions, Laplace transform, Padé expansion, artificial boundary methods.
AB - <p style="text-align: justify;">In this paper we consider the numerical solutions of the fractional diffusion
equation on the unbounded spatial domain. With the application of Laplace transformation,
we obtain one-way equations which absorb the wave touching on the artificial
boundaries. By using Padé expansion to approximate the frequency in Laplace space
and introducing auxiliary variables to reduce the order of the derivatives with respect
to time $t,$ we achieve a system of ODEs within the artificial boundaries. This system
of ODEs, called high-order local absorbing boundary conditions (LABCs), reformulate
the fractional diffusion problem on the unbounded domain to an initial-boundary-value
(IBV) problem on a bounded computational domain. A fully discrete implicit
difference scheme is constructed for the reduced problem. The stability and convergence
rate are established for a finite difference scheme. Finally, numerical experiments
are given to demonstrate the efficiency and accuracy of our approach.</p>