Spectral approximation of time windows in the solution of dissipative linear differential equations

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We establish a relation between the length T of the integration window of a linear differential equation x′ + Ax = b and a spectral parameter s*. This parameter is determined by comparing the exact solution x(T) at the end of the integration window to the solution of a linear system obtained from the Laplace transform of the differential equation by freezing the system matrix. We propose a method to integrate the relation s* = s*(T) into the determination of the interval of rapid convergence of waveform relaxation iterations. The method is illustrated with a few numerical examples.

Original languageEnglish (US)
Pages (from-to)41-64
Number of pages24
JournalJournal of Numerical Analysis, Industrial and Applied Mathematics
Volume4
Issue number1-2
StatePublished - Jul 23 2009

Keywords

  • Linear differential systems
  • Spectral approximation
  • Time window
  • Waveform relaxation

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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