A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel
Type
ArticleAuthors
Ketcheson, David I.
Waheed, Umair bin

KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Solar Center (KSC)
Numerical Mathematics Group
Physical Science and Engineering (PSE) Division
Date
2014-06-13Permanent link to this record
http://hdl.handle.net/10754/333641
Metadata
Show full item recordAbstract
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 wellknown 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
A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel 2014, 9 (2):175 Communications in Applied Mathematics and Computational SciencePublisher
Mathematical Sciences PublishersarXiv
1305.6165Additional Links
http://msp.org/camcos/2014/9-2/p01.xhtmlhttp://github.com/ketch/high_order_RK_RR/
http://arxiv.org/abs/1305.6165
ae974a485f413a2113503eed53cd6c53
10.2140/camcos.2014.9.175