High-order local absorbing boundary conditions for heat equation in unbounded domains

Xiaonan WU*, Jiwei Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

27 Citations (Scopus)


With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions (ABCs) for heat equation. We proved that the coupled system yields a stable problem between the obtained high-order local ABCs and the partial differential equation in the computational domain. This method has been used widely in wave propagation models only recently. We extend the spirit of the methodology to parabolic ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. Some numerical tests show that the new treatment is very efficient and tractable.

Original languageEnglish
Pages (from-to)74-90
Number of pages17
JournalJournal of Computational Mathematics
Issue number1
Publication statusPublished - Jan 2011

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Absorbing boundary conditions
  • Heat equation
  • High-order method
  • Parabolic problems in unbounded domains


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