Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations

Zdzislaw Jackiewicz, S. Tracogna

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

A general class of variable stepsize continuous two-step Runge-Kutta methods is investigated. These methods depend on stage values at two consecutive steps. The general convergence and order criteria are derived and examples of methods of order p and stage order q = p or q = p - 1 are given for p ≤ 5. Numerical examples are presented which demonstrate that high order and high stage order are preserved on nonuniform meshes with large variations in ratios between consecutive stepsizes.

Original languageEnglish (US)
Pages (from-to)347-368
Number of pages22
JournalNumerical Algorithms
Volume12
Issue number3-4
StatePublished - Jul 1996

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Two-step Runge-Kutta Methods
Variable Step Size
Runge Kutta methods
Ordinary differential equations
Ordinary differential equation
Consecutive
Non-uniform Mesh
Higher Order
Numerical Examples
Demonstrate

Keywords

  • Continuous two-step Runge-Kutta method
  • Convergence
  • Order and stage order

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations. / Jackiewicz, Zdzislaw; Tracogna, S.

In: Numerical Algorithms, Vol. 12, No. 3-4, 07.1996, p. 347-368.

Research output: Contribution to journalArticle

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