@Article{CiCP-21-16, author = {}, title = {Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {1}, pages = {16--39}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0033}, url = {http://global-sci.org/intro/article_detail/cicp/11230.html} }