Parallel iterated methods based on variable step-size multistep Runge-Kutta methods of Radau type for stiff problems

Burrage, K. and Suhartanto, H. (2000) Parallel iterated methods based on variable step-size multistep Runge-Kutta methods of Radau type for stiff problems. Advances in Computational Mathematics, 13 3: 257-270. doi:10.1023/A:1018906311204


Author Burrage, K.
Suhartanto, H.
Title Parallel iterated methods based on variable step-size multistep Runge-Kutta methods of Radau type for stiff problems
Journal name Advances in Computational Mathematics   Check publisher's open access policy
ISSN 1019-7168
1572-9044
Publication date 2000-07
Sub-type Article (original research)
DOI 10.1023/A:1018906311204
Volume 13
Issue 3
Start page 257
End page 270
Total pages 14
Editor C. A. Micchelli
Place of publication Basel, Switzerland
Publisher Kluwer Academic Publishers Group
Collection year 2000
Language eng
Subject C1
230116 Numerical Analysis
780101 Mathematical sciences
Formatted abstract
In our previous paper, the performance of a variable step‐size implementation of Parallel Iterated Methods based on Multistep Runge–Kutta methods (PIMRK) is far from satisfactory. This is due to the fact that the underlying parameters of the Multistep Runge–Kutta (MRK) method, and the splitting matrices W that are needed to solve the nonlinear system are designed on a fixed step‐size basis. Similar unsatisfactory results based on this method were also noted by Schneider, who showed that the method is only suitable when the step‐size does not vary too often. In this paper, we design the Variable step‐size Multistep Runge–Kutta (VMRK) method as the underlying formula for Parallel Iterated methods. The numerical results show that Parallel Iterated Variable step‐size MRK (PIVMRK) methods improve substantially on the PIMRK methods and are usually competitive with Parallel Iterated Runge–Kutta methods (PIRKs).
© J.C. Baltzer AG, Science Publishers
Keyword Mathematics, Applied
Ordinary Differential-equations
Q-Index Code C1
Additional Notes Article note: "This revised version was published online in June 2006 with corrections to the Cover Date."

Document type: Journal Article
Sub-type: Article (original research)
Collection: Institute for Molecular Bioscience - Publications
 
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Created: Tue, 10 Jun 2008, 10:50:18 EST