Two-step Runge-Kutta: Theory and practice

S. Tracogna; Bruno Welfert

doi:10.1023/A:1022352704635

Two-step Runge-Kutta: Theory and practice

S. Tracogna, Bruno Welfert

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

Local and global error for Two-Step Runge-Kutta (TSRK) methods are analyzed using the theory of B-series. Global error bounds are derived in both constant and variable stepsize environments. An embedded TSRK pair is constructed and compared with the RK5(4)6M pair of Dormand and Prince on the DETEST set of problems. Numerical results show that the TSRK performs competitively with the RK method.

Original language	English (US)
Pages (from-to)	775-799
Number of pages	25
Journal	BIT Numerical Mathematics
Volume	40
Issue number	4
DOIs	https://doi.org/10.1023/A:1022352704635
State	Published - Dec 2000

Keywords

B-series
Embedded formula
Global error bounds
Local error estimation
Runge-Kutta methods
Two-Step Runge-Kutta methods
Variable step

ASJC Scopus subject areas

Software
Computer Networks and Communications
Computational Mathematics
Applied Mathematics

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10.1023/A:1022352704635

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AB - Local and global error for Two-Step Runge-Kutta (TSRK) methods are analyzed using the theory of B-series. Global error bounds are derived in both constant and variable stepsize environments. An embedded TSRK pair is constructed and compared with the RK5(4)6M pair of Dormand and Prince on the DETEST set of problems. Numerical results show that the TSRK performs competitively with the RK method.

KW - B-series

KW - Embedded formula

KW - Global error bounds

KW - Local error estimation

KW - Runge-Kutta methods

KW - Two-Step Runge-Kutta methods

KW - Variable step

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Two-step Runge-Kutta: Theory and practice

Abstract

Keywords

ASJC Scopus subject areas

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