Convergence of waveform relaxation methods for differential-algebraic systems

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44 Scopus citations

Abstract

This paper gives sufficient conditions for existence and uniqueness of solutions and for the convergence of Picard iterations and more general waveform relaxation methods for differential-algebraic systems of neutral type. The results are obtained by the contraction mapping principle on Banach spaces with weighted norms and by the use of the Perron-Frobenius theory of nonnegative and nonreducible matrices. It is demonstrated that waveform relaxation methods are convergent faster than the classical Picard iterations.

Original languageEnglish (US)
Pages (from-to)2303-2317
Number of pages15
JournalSIAM Journal on Numerical Analysis
Volume33
Issue number6
DOIs
StatePublished - Dec 1996

Keywords

  • Differential-algebraic system
  • Picard iterations
  • Waveform relaxation

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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