Variations on a theme by Euler

Journal of Computational Mathematics

Volumn 16, Issue 2, 1998, Pages 97-106

  Feng, Kang ^a   Wang, Dao Liu ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Explicit Euler method; Hamiltonian systems; Nilpotent; Symplectic difference schemes; Symplectically separable

Indexed keywords

EID: 0012686870     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. V.I. Arnold, Mathematical Methods of Classical Mechanics, New York: Springer. 1978.
2. V.V. Beloshapkin, A.A. Chernikov, M. Natenzon, B.A. Petrovichev, R.Z. Sagdeev, G.M. Zaslavsky, Chaotic streamlines in pre-turbulent states, Nature, 337:12 (1989), 133-137.
3. P.J. Channell, J.C. Scovel, Symplectic Integration of Hamiltonian Systems, Nonlinearity, 3 (1990), 213.
4. A.A. Chernikov, R.Z. Sagdeev, G.M. Zaslavsky, Stochastic Webs, Physica D, 33 (1988), 65-76.
5. K. Feng, On difference schemes and symplectic geometry, In Feng K, ed. Proc 1984 Beijing Symp Diff Geometry and Diff Equations. Beijing: Science Press, (1985), 42-58.
6. K. Feng, Difference schemes for Hamiltonian formalism and symplectic geometry, J. Comp. Math., 4:3: (1986), 279-289.
7. K. Feng, The Hamiltonian way for computing Hamiltonian dynamics, In Spigler R, ed. Applied and Industrial Mathematics. Netherlands: Kluwer, (1991), 17-35.
8. K. Feng, How to compute properly Newton's equation of motion, In Ying L A, Guo B Y, ed. Proc of 2nd Conf on Numerical Methods for Partial Differential Equations, Singapore: World Scientific, (1992), 15-22.
9. K. Feng, Formal dynamical systems and numerical algorithms, In Feng K, Shi Z C, ed. Proc Inter Conf on Computation of Differential Equations and Dynamical Systems, Singapore: World Scientific, (1993), 1-10.
10. K. Feng, The step transition operators for multi-step methods of ODE's: [Preprint]. Beijing: GAS. Computing Center, 1991.
11. K. Feng, The calculus of generating functions and the formal energy for Hamiltonian algorithms: [Preprint]. Beijing: GAS. Computing Center, 1991.
12. K. Feng, M.Z. Qin, The symplectic methods for computation of Hamiltonian equations. In Zhu Y L, Guo Ben-yu, ed. Proc Conf on Numerical Methods for PDE's. Berlin: Springer, 1987. 1-37. Lect Notes in Math 1297.
13. K. Feng, M.Z. Qin, Hamiltonian algorithms and a comparative numerical study, Comput Phys Comm., 65 (1991), 173-187.
14. K. Feng, D.L. Wang, A note on conservation laws of symplectic difference schemes for Hamiltonian systems, J. Comp. Math., 9:3 (1991), 229-237.
15. K. Feng, H.M. Wu, M.Z. Qin, D.L. Wang, Construction of canonical difference schemes for Hamiltonian formalism via generating functions, J. Comp. Math., 7:1, (1989), 71-96.
16. Z. Ge, K. Feng, On the approximation of Hamiltonian systems, J. Comp. Math., 6:1 (1988), 88-97.
17. Z. Ge, J. Marsden, Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators, Phys Lett A., 133:3 (1988), 137-139.
18. M.Z. Qin, D.L. Wang, M.Q. Zhang, Explicit symplectic difference schemes for separable Hamiltonian systems, J. Comp. Math., 9:3 (1991), 211-221.
19. M.Z. Qin, W.J. Zhu, Construction of higher order symplectic schemes by composition, Computing, 47 (1992), 309-321.
20. D.L. Wang, Some aspects of Hamiltonian systems and symplectic algorithms, Physica D, 73 (1994), 1-16.
21. Y.H. Wu, The generating function of the solution of ODE and its discrete methods, Computer Math. Applic., 15:12 (1988), 1041-1050.
22. Y.H. Wu, Symplectic transformations and symplectic difference schemes, Chinese J. Numer. Math. Applic., 12:1 (1990), 23-31.
23. H. Yoshida, Construction of higher order symplectic integrators, Phys. Letters A, 150 (1990), 262-268.