A-stable diagonally implicit Runge-Kutta-Nyström methods for parallel computers |
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Authors: | Nguyen huu Cong |
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Affiliation: | (1) Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands;(2) Faculty of Mathematics, Mechanics and Informatics, University of Hanoi, Thuong dinh, Dong Da, Hanoi, Vietnam |
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Abstract: | In this paper, we study diagonally implicit Runge-Kutta-Nyström methods (DIRKN methods) for use on parallel computers. These methods are obtained by diagonally implicit iteration of fully implicit Runge-Kutta-Nyström methods (corrector methods). The number of iterations is chosen such that the method has the same order of accuracy as the corrector, and the iteration parameters serve to make the method at least A-stable. Since a large number of the stages can be computed in parallel, the methods are very efficient on parallel computers. We derive a number of A-stable, strongly A-stable and L-stable DIRKN methods of orderp withs* (p) sequential, singly diagonal-implicit stages wheres*(p)=[(p+1)/2] ors* (p)=[(p+1)/2]+1,[°] denoting the integer part function.These investigations were supported by the University of Amsterdam with a research grant to enable the author to spend a total of two years in Amsterdam. |
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Keywords: | Diagonally implicit Runge-Kutta-Nyströ m methods predictor-corrector methods parallelism |
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