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Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain
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Year:    2017

Communications in Computational Physics, Vol. 21 (2017), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2016-0033

Communications in Computational Physics, Vol. 21 (2017), Iss. 1 : pp. 16–39

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:   

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