Convergence of waveform relaxation methods for differential-algebraic systems

Research output: Contribution to journalArticle

43 Citations (Scopus)

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
StatePublished - Dec 1996

Fingerprint

Waveform Relaxation Method
Picard Iteration
Differential-algebraic Systems
Banach spaces
Perron-Frobenius Theory
Contraction Mapping Principle
Weighted Norm
Neutral Type
Existence and Uniqueness of Solutions
Non-negative
Banach space
Sufficient Conditions

Keywords

  • Differential-algebraic system
  • Picard iterations
  • Waveform relaxation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Convergence of waveform relaxation methods for differential-algebraic systems. / Jackiewicz, Zdzislaw; Kwapisz, M.

In: SIAM Journal on Numerical Analysis, Vol. 33, No. 6, 12.1996, p. 2303-2317.

Research output: Contribution to journalArticle

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