Symmetric general linear methods

J. C Butcher, A. T. Hill, T. J. T. Norton

Research output: Contribution to journalArticle

5 Citations (Scopus)
64 Downloads (Pure)

Abstract

The article considers symmetric general linear methods, a class of numerical time integration methods which, like symmetric Runge–Kutta methods, are applicable to general time-reversible differential equations, not just those derived from separable second-order problems. A definition of time-reversal symmetry is formulated for general linear methods, and criteria are found for the methods to be free of linear parasitism. It is shown that symmetric parasitism-free methods cannot be explicit, but such a method of order 4 is constructed with only one implicit stage. Several characterizations of symmetry are given, and connections are made with G-symplecticity. Symmetric methods are shown to be of even order, a suitable symmetric starting method is constructed and shown to be essentially unique. The underlying one-step method is shown to be time-symmetric.
Original languageEnglish
Pages (from-to)1189-1212
Number of pages24
JournalBIT Numerical Mathematics
Volume56
Issue number4
Early online date22 Mar 2016
DOIs
Publication statusPublished - 1 Dec 2016

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General Linear Methods
Runge Kutta methods
Differential equations
Symmetry
One-step Method
Time Reversal
Time Integration
Runge-Kutta Methods
Differential equation

Keywords

  • Time-symmetric general linear methods
  • G-symplectic methods · Multivalue methods
  • Conservative methods

Cite this

Symmetric general linear methods. / Butcher, J. C; Hill, A. T.; Norton, T. J. T.

In: BIT Numerical Mathematics, Vol. 56, No. 4, 01.12.2016, p. 1189-1212.

Research output: Contribution to journalArticle

Butcher, J. C ; Hill, A. T. ; Norton, T. J. T. / Symmetric general linear methods. In: BIT Numerical Mathematics. 2016 ; Vol. 56, No. 4. pp. 1189-1212.
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