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Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

Part of:Integral equations, integral transformsLinear integral equationsNumerical approximation and computational geometry

Published online by Cambridge University Press:  05 December 2016

Wei Zhang,
Jiang Yang,
Jiwei Zhang and
Qiang Du
Wei Zhang*
Affiliation:
Beijing Computational Science Research Centre, Beijing, P.R. China
Jiang Yang*
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA
Jiwei Zhang*
Affiliation:
Beijing Computational Science Research Centre, Beijing, P.R. China
Qiang Du*
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA
*
*Corresponding author. Email addresses:wzhang@csrc.ac.cn (W. Zhang), jyanghkbu@gmail.com (J. Yang), jwzhang@csrc.ac.cn (J. Zhang), qd2125@columbia.edu (Q. Du)
*Corresponding author. Email addresses:wzhang@csrc.ac.cn (W. Zhang), jyanghkbu@gmail.com (J. Yang), jwzhang@csrc.ac.cn (J. Zhang), qd2125@columbia.edu (Q. Du)
*Corresponding author. Email addresses:wzhang@csrc.ac.cn (W. Zhang), jyanghkbu@gmail.com (J. Yang), jwzhang@csrc.ac.cn (J. Zhang), qd2125@columbia.edu (Q. Du)
*Corresponding author. Email addresses:wzhang@csrc.ac.cn (W. Zhang), jyanghkbu@gmail.com (J. Yang), jwzhang@csrc.ac.cn (J. Zhang), qd2125@columbia.edu (Q. Du)

Abstract

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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.

Keywords

Artificial boundary conditionsnonlocal modelsPadé approximationnonlocal heat equationsartificial boundary method

MSC classification

Secondary:45A05: Linear integral equations65D99: None of the above, but in this section65R20: Integral equations

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 1 , January 2017, pp. 16 - 39
Copyright
Copyright © Global-Science Press 2016 

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