Paper Info
Title
New Integration Methods for Perturbed ODEs Based on Symplectic Implicit Runge-Kutta Schemes with Application to Solar System Simulations.
Abstract
We propose a family of integrators, flow-composed implicit Runge–Kutta methods, for perturbations of nonlinear ordinary differential equations, consisting of the composition of flows of the unperturbed part alternated with one step of an implicit Runge–Kutta (IRK) method applied to a transformed system. The resulting integration schemes are symplectic when both the perturbation and the unperturbed part are Hamiltonian and the underlying IRK scheme is symplectic. In addition, they are symmetric in time (resp. have order of accuracy r) if the underlying IRK scheme is time-symmetric (resp. of order r). The proposed new methods admit mixed precision implementation that allows us to efficiently reduce the effect of round-off errors. We particularly focus on the potential application to long-term solar system simulations, with the equations of motion of the solar system rewritten as a Hamiltonian perturbation of a system of uncoupled Keplerian equations. We present some preliminary numerical experiments with a simple point mass Newtonian 10-body model of the solar system (with the sun, the eight planets, and Pluto) written in canonical heliocentric coordinates.
Year
DOI
Venue
2018
10.1007/s10915-017-0634-1
J. Sci. Comput.
Keywords
Field
DocType
Symplectic implicit Runge–Kutta schemes, Solar system simulations, Efficient implementation, Mixed precision, Round-off error propagation
Runge–Kutta methods,Order of accuracy,Hamiltonian (quantum mechanics),Mathematical analysis,Symplectic geometry,Point particle,Equations of motion,Ode,Mathematics,Perturbation (astronomy)
Journal
Volume
Issue
ISSN
76
1
0885-7474
Citations 
PageRank 
References 
0
0.34
12
Authors
3
Name
Order
Citations
PageRank
Mikel Antoñana100.34
J. Makazaga2112.53
A. Murua311025.21