IJPAM: Volume 40, No. 3 (2007)


H.L. Su$^1$, Y.J. Sun$^2$, M.Z. Qin$^3$, R. Scherer$^4$
$^1$Department of Mathematics
Remin University
Beijing, 100080, P.R. CHINA
$^{2,3}$Institute of Computational Mathematics and
Scientific/Engineering Computing
Academy of Mathematics and System Sciences
Academic Sinica
B.O. Box 2719, Beijing, 100080, P.R. CHINA
$^3$e-mail: [email protected]
$^4$Institute of Applied and Numerical Mathematics
University of Karlsruhe
Karlsruhe, 76128, GERMANY
e-mail: [email protected]

Abstract.A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this paper the symplectic geometry structure of Birkhoffian system is discussed, then the symplecticity of Birkhoffian phase flow is presented. Based on these properties, a way to construct symplectic schemes for Birkhoffian systems by using the generating function method is explained.

Received: August 12, 2007

AMS Subject Classification: 65P10

Key Words and Phrases: Birkhoffian system, method of generating function, symplectic difference schemes, linear and semilinear oscillator equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 3