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arXiv · 1507.00535

Volume Preservation by Runge-Kutta Methods

Philipp Bader·David I McLaren·G. R. W. Quispel·Marcus Webb
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Abstract

It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge-Kutta method will respect this property for such systems, but it has been shown that no B-Series method can be volume preserving for all volume preserving vector fields (BIT 47 (2007) 351-378 and IMA J. Numer. Anal. 27 (2007) 381-405). In this paper we show that despite this result, symplectic Runge-Kutta methods can be volume preserving for a much larger class of vector fields than Hamiltonian systems, and discuss how some Runge-Kutta methods can preserve a modified measure exactly.

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Philipp Bader, David I McLaren, G. R. W. Quispel, Marcus Webb. 2015-07-02. Volume Preservation by Runge-Kutta Methods. https://arxiv.org/abs/1507.00535

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