Global Error Control in the Runge-Kutta Solution of a Hamiltonian System using the RKQ Algorithm
Numerical Analysis
2011-12-01 v1
Abstract
We study the effect of global error control in the numerical solution of Hamiltonian systems. In particular, we apply the RKQ algorithm in the numerical solution of a Hamiltonian system. This algorithm is designed to provide stepwise control of both local and global error. A test problem demonstrates the error control features of RKQ. Good results are obtained, despite the fact that explicit Runge-Kutta methods have been used in RKQ, rather than symplectic Runge-Kutta methods. This simply emphasizes the value of stepwise global error control, as per the RKQ algorithm.
Cite
@article{arxiv.1111.6996,
title = {Global Error Control in the Runge-Kutta Solution of a Hamiltonian System using the RKQ Algorithm},
author = {J. S. C. Prentice},
journal= {arXiv preprint arXiv:1111.6996},
year = {2011}
}