Volume preservation by Runge–Kutta methods
Copyright policy )Volume preservation by Runge–Kutta methods
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.
17 pages, as submitted to journal
- University of Manchester United Kingdom
- University of Cambridge United Kingdom
- UNIVERSITY OF CAMBRIDGE
- University of Manchester United Kingdom
- La Trobe University Australia
volume preservation, Measure preservation, measure preservation, 4904 Pure Mathematics, Numerical Analysis (math.NA), Kahan's method, Numerical methods for Hamiltonian systems including symplectic integrators, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Volume preservation, 49 Mathematical Sciences, FOS: Mathematics, Runge-Kutta method, Mathematics - Numerical Analysis
volume preservation, Measure preservation, measure preservation, 4904 Pure Mathematics, Numerical Analysis (math.NA), Kahan's method, Numerical methods for Hamiltonian systems including symplectic integrators, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Volume preservation, 49 Mathematical Sciences, FOS: Mathematics, Runge-Kutta method, Mathematics - Numerical Analysis
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