The Relative Efficiency of Quenching and Reintegration for Global Error Control in Runge-Kutta Methods
Abstract
We compare the efficiency of two algorithms for controlling global error in Runge-Kutta methods, i.e. reintegration and RKQ. We find that RKQ (which uses a quenching strategy) is, on average, more efficient than reintegration, by at least 16% or 30%, depending on the form of RKQ. Some numerical examples indicate that larger gains in efficiency are possible. The Runge-Kutta methods we consider are explicit, implicit (Radau, Lobatto, Gauss), embedded and Nyström.
Copyright © 2012 J.S.C. Prentice. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
J. S. C. Prentice, The Relative Efficiency of Quenching and Reintegration for Global Error Control in Runge-Kutta Methods, J. Math. Comput. Sci. 2 (2012), 880–888.
BibTeX
@article{Prentice2012,
author = {Prentice, J.S.C.},
title = {The Relative Efficiency of Quenching and Reintegration for Global Error Control in Runge-Kutta Methods},
journal = {J. Math. Comput. Sci.},
volume = {2},
year = {2012},
pages = {880--888},
doi = {}
}