Eigenvalue analysis for summation-by-parts finite difference time discretizations

Andrea Alessandro Ruggiu, Jan Nordström

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Diagonal norm finite difference based time integration methods in summation-by-parts form are investigated. The second, fourth, and sixth order accurate discretizations are proven to have eigenvalues with strictly positive real parts. This leads to provably invertible fully discrete approximations of initial boundary value problems. Our findings also allow us to conclude that the Runge-Kutta methods based on second, fourth, and sixth order summation-by-parts finite difference time discretizations automatically satisfy previously unreported stability properties. The procedure outlined in this article can be extended to even higher order summation-by-parts approximations with repeating stencil.

Original languageEnglish
Pages (from-to)907-928
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume58
Issue number2
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Eigenvalue problem
  • Finite difference methods
  • Initial value problem
  • Summation-by-parts operators
  • Time integration

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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