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Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

  • Wei Zhang (a1), Jiang Yang (a2), Jiwei Zhang (a1) and Qiang Du (a2)
Abstract
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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Corresponding author
*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)
References
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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