The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged Vector Field method
Numerical Analysis
2012-03-16 v1
Abstract
No Runge-Kutta method can be energy preserving for all Hamiltonian systems. But for problems in which the Hamiltonian is a polynomial, the Averaged Vector Field (AVF) method can be interpreted as a Runge-Kutta method whose weights and abscissae represent a quadrature rule of degree at least that of the Hamiltonian. We prove that when the number of stages is minimal, the Runge-Kutta scheme must in fact be identical to the AVF scheme.
Keywords
Cite
@article{arxiv.1203.3252,
title = {The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged Vector Field method},
author = {Elena Celledoni and Brynjulf Owren and Yajuan Sun},
journal= {arXiv preprint arXiv:1203.3252},
year = {2012}
}