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The Scientific World Journal
Volume 2014, Article ID 147801, 7 pages
http://dx.doi.org/10.1155/2014/147801
Research Article

Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received 10 January 2014; Accepted 3 March 2014; Published 1 April 2014

Academic Editors: M. Han, Z. Jin, and Y. Xia

Copyright © 2014 Y. H. Cong and C. X. Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods.