Structure-preserving properties of three differential schemes for oscillator system.pdf

Appl. Math. Mech. -Engl. Ed., 35(6), 783–790 (2014) Applied Mathematics DOI 10.1007/s10483-014-1828-6 and Mechanics c Shanghai University and Springer-Verlag Berlin Heidelberg 2014 (English Edition) Structure-preserving properties of three differential schemes for oscillator system∗ 1 1,2 1,2 Yu-yue QIN (‹ u ) , Zi-chen DENG ( f˜ ) , Wei-peng HU (•+ ) (1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, P. R. China; 2. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, Liaoning Province, P. R. China) Abstract A numerical method for the Hamiltonian system is required to preserve some structure-preserving properties. The current structure-preserving method satisfies the requirements that a symplectic method can preserve the symplectic structure of a finite dimension Hamiltonian system, and a multi-symplectic method can preserve the multi-symplectic structure of an infinite dimension Hamiltonian system. In this paper, the structure-preserving properties of three differential schemes for an oscillator system are investigated in detail. Both the theoretical results and the numerical results show that the results obtained by the standard forward Euler scheme lost all the three geo- metric properties of the oscillator system, i.e.