# Preserving first integrals and volume forms of additively split systems

@article{Chartier2007PreservingFI,
title={Preserving first integrals and volume forms of additively split systems},
author={Philippe Chartier and Ander Murua},
journal={Ima Journal of Numerical Analysis},
year={2007},
volume={27},
pages={381-405}
}
• Published 1 April 2007
• Mathematics
• Ima Journal of Numerical Analysis
This work is concerned with the preservation of invariants and volume forms by numerical methods which can be expanded into B-series. The situation we consider here is that of a split vector field f = f [1] +... + f [N] , where each f [ν] either has the common invariant I or is divergence-free. We derive algebraic conditions on the coefficients of the B-series for it either to preserve I or to preserve the volume for generic vector fields and interpret them for additive Runge-Kutta methods…

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