Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain (Communications in Computational Physics, 2018)
This paper is concerned with numerical approximations of a nonlocal heatequation 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 ABCsreformulate the original problem into an initial-boundary-value (IBV) problem on abounded domain. For the global ABCs, we adopt a fast evolution to enhance computationalefficiency 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 efficiencyof the proposed methods.