Two-step Runge-Kutta methods

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

Implicit two-step Runge-Kutta methods are studied. It will be shown that these methods require fewer stages to achieve the same order as one-step Runge-Kutta methods, which means the two-step methods are potentially more efficient than one-step methods. Order conditions are derived and examples of two-step one-stage methods of order 2 and two-step two-stage methods of order 4 are presented. Stability properties of these methods with respect to y′ = ay are studied and A-stable two-step methods of order 2 are characterized. Two-step two-stage methods of order 4 which are A-stable are found by an extensive computer search. Semi-implicit two-stage methods of order 4 were also constructed. This is in contrast to the situation encountered in the Runge-Kutta theory where the unique two-stage method of order 4 is not semi-implicit.

Original languageEnglish (US)
Pages (from-to)1165-1182
Number of pages18
JournalSIAM Journal on Numerical Analysis
Volume28
Issue number4
StatePublished - Aug 1991

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Two-step Runge-Kutta Methods
Runge Kutta methods
One-step Method
Two-step Method
Semi-implicit
Order Conditions
Implicit Method
Runge-Kutta
Runge-Kutta Methods

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Two-step Runge-Kutta methods. / Jackiewicz, Zdzislaw; Renaut, Rosemary; Feldstein, A.

In: SIAM Journal on Numerical Analysis, Vol. 28, No. 4, 08.1991, p. 1165-1182.

Research output: Contribution to journalArticle

Jackiewicz, Z, Renaut, R & Feldstein, A 1991, 'Two-step Runge-Kutta methods', SIAM Journal on Numerical Analysis, vol. 28, no. 4, pp. 1165-1182.
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