Contractivity of waveform relaxation Runge-Kutta iterations and related limit methods for dissipative systems in the maximum norm

A. Bellen, Zdzislaw Jackiewicz, M. Zennaro

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

Contractivity properties of Runge-Kutta methods are analyzed, with suitable interpolation implemented using waveform relaxation strategy for systems of ordinary differential equations that are dissipative in the maximum norm. In general, this type of implementation, which is quite appropriate in a parallel computing environment, improves the stability properties of Runge-Kutta methods. As a result of this analysis, a new class of methods is determined, which is different from Runge-Kutta methods but closely related to them, and which combines its high order of accuracy and unconditional contractivity in the maximum norm. This is not possible for classical Runge-Kutta methods.

Original languageEnglish (US)
Pages (from-to)499-523
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume31
Issue number2
StatePublished - Apr 1994
Externally publishedYes

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Waveform Relaxation
Contractivity
Maximum Norm
Runge Kutta methods
Dissipative Systems
Runge-Kutta
Runge-Kutta Methods
Iteration
Convergence of numerical methods
Parallel processing systems
Parallel Computing
System of Ordinary Differential Equations
Ordinary differential equations
Interpolation
Interpolate
Higher Order

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

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AU - Zennaro, M.

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