Rational approximations to 1/√1 - s2, one-way wave equations and absorbing boundary conditions

Rosemary Renaut, J. S. Parent

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

One-way wave equations (OWWEs), derived from rational approximations, C(s) to 1/√1 - s2, are considered. Absorbing boundary conditions obtained from these OWWEs are easily implemented, producing systems of differential equations at the boundary which are different from those produced by rational approximations, r(s) to √1 - s2. Although these systems are different, a particular choice of difference approximation for the system yields numerical methods such that stability properties of both approaches are equivalent. In particular, for C(s) = 1/r(s), the two systems possess equivalent stability properties. In other cases, numerical results are presented which demonstrate that, where C(s) and r(s) are not derived via interpolation, the C(s) OWWEs can provide better absorption.

Original languageEnglish (US)
Pages (from-to)245-259
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume72
Issue number2
DOIs
StatePublished - Aug 13 1996

Keywords

  • Absorbing boundary conditions
  • Discrete approximations
  • One-way wave equations
  • Stability
  • Well-posedness

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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