Translator Disclaimer
2014 A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel
David Ketcheson, Umair bin Waheed
Commun. Appl. Math. Comput. Sci. 9(2): 175-200 (2014). DOI: 10.2140/camcos.2014.9.175

Abstract

We compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge–Kutta pairs. We consider orders four through twelve, including both serial and parallel implementations. We cast extrapolation and deferred correction methods as fixed-order Runge–Kutta methods, providing a natural framework for the comparison. The stability and accuracy properties of the methods are analyzed by theoretical measures, and these are compared with the results of numerical tests. In serial, the eighth-order pair of Prince and Dormand (DOP8) is most efficient. But other high-order methods can be more efficient than DOP8 when implemented in parallel. This is demonstrated by comparing a parallelized version of the well-known ODEX code with the (serial) DOP853 code. For an N-body problem with N=400, the experimental extrapolation code is as fast as the tuned Runge–Kutta pair at loose tolerances, and is up to two times as fast at tight tolerances.

Citation

Download Citation

David Ketcheson. Umair bin Waheed. "A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel." Commun. Appl. Math. Comput. Sci. 9 (2) 175 - 200, 2014. https://doi.org/10.2140/camcos.2014.9.175

Information

Received: 4 November 2013; Revised: 4 May 2014; Accepted: 8 May 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1314.65102
MathSciNet: MR3326136
Digital Object Identifier: 10.2140/camcos.2014.9.175

Subjects:
Primary: 65L06
Secondary: 65Y05

Rights: Copyright © 2014 Mathematical Sciences Publishers

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.9 • No. 2 • 2014
MSP
Back to Top