论文信息 - Non-existence of the modified first integral by symplectic integration methods

Non-existence of the modified first integral by symplectic integration methods

Abstract It is known that the symplectic mapping obtained as a symplectic integration method is formally an exact time evolution of the modified Hamiltonian which is close to the original Hamiltonian. In the case when the original Hamiltonian has an additional first integral, it is shown that the modified first integral, which is defined to be an integral for the modified Hamiltonian, does not necessarily exist in general. This non-existence of the modified first integral is demonstrated by an example of the 2D harmonic oscillator with an integer frequency ratio.

Haruo Yoshida | H. Yoshida

[1] Ernst Hairer,et al. The life-span of backward error analysis for numerical integrators , 1997 .

[2] J. M. Sanz-Serna,et al. Numerical Hamiltonian Problems , 1994 .

[3] H. Yoshida. Construction of higher order symplectic integrators , 1990 .

[4] Robert I. McLachlan,et al. On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods , 1995, SIAM J. Sci. Comput..

[5] Existence of formal integrals of symplectic integrators , 1995 .

[6] G. Benettin,et al. On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms , 1994 .

[7] V. Varadarajan. Lie groups, Lie algebras, and their representations , 1974 .

[8] M. F. Ranada. Superintegrable n=2 systems, quadratic constants of motion, and potentials of Drach , 1997 .

[9] Haruo Yoshida,et al. Recent progress in the theory and application of symplectic integrators , 1993 .

[10] P. Hartman. Ordinary Differential Equations , 1965 .

[11] E. Hairer,et al. Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .