Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs, i

Saul S. Abarbanel, Alina E. Chertock

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

Temporal, or "strict," stability of approximation to PDEs is much more difficult to achieve than the "classical" Lax stability. In this paper, we present a class of finite-difference schemes for hyperbolic initial boundary value problems in one and two space dimensions that possess the property of strict stability. The approximations are constructed so that all eigenvalues of corresponding differentiation matrix have a nonpositive real part. Boundary conditions are imposed by using penalty-like terms. Fourth- and sixth-order compact implicit finite-difference schemes are constructed and analyzed. Computational efficacy of the approach is corroborated by a series of numerical tests in 1-D and 2-D scalar problems.

Original languageEnglish
Pages (from-to)42-66
Number of pages25
JournalJournal of Computational Physics
Volume160
Issue number1
DOIs
StatePublished - 1 May 2000
Externally publishedYes

Keywords

  • Accuracy
  • Boundary conditions
  • Error bounds
  • Hyperbolic PDEs
  • Stability

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