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BIT Numerical Mathematics

Erschienen in:

01.12.2016

Symmetric general linear methods

verfasst von: J. C. Butcher, A. T. Hill, T. J. T. Norton

Erschienen in: BIT Numerical Mathematics | Ausgabe 4/2016

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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.

Vorheriger Artikel Bivariate hierarchical Hermite spline quasi-interpolation

Nächster Artikel Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems

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Titel: Symmetric general linear methods
verfasst von: J. C. Butcher
A. T. Hill
T. J. T. Norton
Publikationsdatum: 01.12.2016
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 4/2016
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-016-0613-1

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