Year: 2000
Author: Shou-Fu Li
Journal of Computational Mathematics, Vol. 18 (2000), Iss. 6 : pp. 645–656
Abstract
The main results of this paper are as follows: (1) Suppose an s stage Runge-Kutta method is consistent, irreducible, non-confluent and symplectic. Then this method is of order at least 2p+l(1≤p≤s−1) provided that the simplifying conditions C(p) (or D(p) with non-zero weights) and B(2p+l) hold, where l=0,1,2. (2) Suppose an s stage Runge-Kutta method is consistent, irreducible and non-confluent, and satisfies the simplifying conditions C(p) and D(p) with 0＜p≤s. Then this method is symplectic if and only if either p=s or the nonlinear stablility matrix M of the method has an (s−p)×(s−p) chief submatrix ˆM=0. (3) Using the results (1) and (2) as bases, we present a general approach for the construction of symplectic Runge-Kutta methods, and a software has benn designed, by means of which, the coefficients of s stage symplectic Runge-Kutta methods satisfying C(p),D(p) and B(2p+l) can be easily computed, where 1≤p≤s,0≤l≤2,s≤2p+l≤2s.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2000-JCM-9075
Journal of Computational Mathematics, Vol. 18 (2000), Iss. 6 : pp. 645–656
Published online: 2000-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Numerical analysis Symplectic Runge-Kutta methods Simplifying conditions Order results.