Stability analysis of runge-kutta methods for volterra integral equations of the second kind

A. Bellen, Zdzislaw Jackiewicz, R. Vermiglio, M. Zennaro

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Stability analysis of Volterra-Runge-Kutta methods based on the basic test equation of the form. y(t)=1+λ∫0ty(s) ds (t≥0),where λ is a complex parameter, and on the convolution test equation. y(t)=1+∫0t[λ+σ(t-s)]y(s)ds (t≥0),where λ and σ are real parameters, is presented. General stability conditions are derived and applied to construct numerical methods with good stability properties. In particular, a family of second-order Vo-stable Volterra-Runge-Kutta methods is obtained. No Vo-stable methods of order greater than one have been presented previously in the literature.

Original languageEnglish (US)
Pages (from-to)103-118
Number of pages16
JournalIMA Journal of Numerical Analysis
Volume10
Issue number1
DOIs
StatePublished - Jan 1990

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Runge-Kutta method
Runge Kutta methods
Volterra Integral Equations
Convergence of numerical methods
Volterra
Runge-Kutta Methods
Integral equations
integral equations
Stability Analysis
Stability Condition
Convolution
Numerical Methods
convolution integrals
Numerical methods
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ASJC Scopus subject areas

  • Molecular Biology
  • Statistics and Probability
  • Computational Mathematics
  • Condensed Matter Physics
  • Applied Mathematics
  • Mathematics(all)

Cite this

Stability analysis of runge-kutta methods for volterra integral equations of the second kind. / Bellen, A.; Jackiewicz, Zdzislaw; Vermiglio, R.; Zennaro, M.

In: IMA Journal of Numerical Analysis, Vol. 10, No. 1, 01.1990, p. 103-118.

Research output: Contribution to journalArticle

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