Functionally fitted explicit pseudo two-step Runge-Kutta methods

Hoang, Nguyen S. and Sidje, Roger B. (2009) Functionally fitted explicit pseudo two-step Runge-Kutta methods. Applied Numerical Mathematics, 59 1: 39-55. doi:10.1016/j.apnum.2007.11.023

Author Hoang, Nguyen S.
Sidje, Roger B.
Title Functionally fitted explicit pseudo two-step Runge-Kutta methods
Journal name Applied Numerical Mathematics   Check publisher's open access policy
ISSN 0168-9274
Publication date 2009-01
Year available 2007
Sub-type Article (original research)
DOI 10.1016/j.apnum.2007.11.023
Volume 59
Issue 1
Start page 39
End page 55
Total pages 17
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Language eng
Abstract Explicit pseudo two-step Runge–Kutta (EPTRK) methods belong to the wider class of general linear multistep methods. The particularity of EPTRK methods is that they do not use the last two iterates as conventional two-step methods do. Rather, they predict the intermediate stage values and combine them with the last iterate to obtain the next iterate. EPTRK methods were initially designed to suit parallel computers, but they have been shown to achieve arbitrary high-order and thus can be useful as conventional explicit RK methods on sequential computers as well. Our contribution in this paper is to present a new family of functionally fitted EPTRK methods aimed at integrating an equation exactly if its solution is a linear combination of a chosen set of basis functions. We use a variation of collocation techniques to show that this new family, which we call FEPTRK, shares the same accuracy properties as EPTRK. The added advantage is that FEPTRK can use specific fitting functions to capitalize on the special properties of the problem that may be known in advance.
Keyword Functionally fitted
variable coefficients
Two-step explicity RK
Nonstiff ODEs
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: Advanced Computational Modelling Centre Publications
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 03 Sep 2009, 09:13:19 EST by Mr Andrew Martlew on behalf of Advanced Computational Modelling Centre