Conservative methods for dynamical systems
Abstract
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and non-autonomous dynamical systems with conserved quantities of arbitrary forms, such as time-dependent conserved quantities. Sufficient conditions to construct conservative schemes of arbitrary order are derived using the multiplier method. General formulas for first-order conservative schemes are constructed using divided difference calculus. New conservative schemes are found for various dynamical systems such as Euler's equation of rigid body rotation, Lotka-Volterra systems, the planar restricted three-body problem and the damped harmonic oscillator.
Keywords
Cite
@article{arxiv.1612.02417,
title = {Conservative methods for dynamical systems},
author = {Andy T. S. Wan and Alexander Bihlo and Jean-Christophe Nave},
journal= {arXiv preprint arXiv:1612.02417},
year = {2018}
}
Comments
29 pages