Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain

Hermann BRUNNER, Houde Han, Dongsheng Yin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

We consider the numerical solution of the time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain. Introduce an artificial boundary and find the exact and approximate artificial boundary conditions for the given problem, which lead to a bounded computational domain. Using the exact or approximating boundary conditions on the artificial boundary, the original problem is reduced to an initial-boundary-value problem on the bounded computational domain which is respectively equivalent to or approximates the original problem. A finite difference method is used to solve the reduced problems on the bounded computational domain. The numerical results demonstrate that the method given in this paper is effective and feasible.

Original languageEnglish
Pages (from-to)541-562
Number of pages22
JournalJournal of Computational Physics
Volume276
DOIs
Publication statusPublished - 1 Nov 2014

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Artificial boundary conditions
  • Numerical solution
  • Time-fractional diffusion-wave equation
  • Unbounded spatial domain

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