TY - JOUR
T1 - Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain
JO - Communications in Computational Physics
VL - 1
SP - 16
EP - 39
PY - 2018
DA - 2018/04
SN - 21
DO - http://doi.org/10.4208/cicp.OA-2016-0033
UR - https://global-sci.org/intro/article_detail/cicp/11230.html
KW - 
AB - <p style="text-align: justify;">This paper is concerned with numerical approximations of a nonlocal heat
equation define on an infinite domain. Two classes of artificial boundary conditions
(ABCs) are designed, namely, nonlocal analog Dirichlet-to-Neumann-type ABCs
(global in time) and high-order Padé approximate ABCs (local in time). These ABCs
reformulate the original problem into an initial-boundary-value (IBV) problem on a
bounded domain. For the global ABCs, we adopt a fast evolution to enhance computational
efficiency and reduce memory storage. High order fully discrete schemes,
both second-order in time and space, are given to discretize two reduced problems.
Extensive numerical experiments are carried out to show the accuracy and efficiency
of the proposed methods.</p>