论文信息 - Symplectic integration of nonlinear Hamiltonian systems

Symplectic integration of nonlinear Hamiltonian systems

There exist several standard numerical methods for integrating ordinary differential equations. However, if one is interested in integration of Hamiltonian systems, these methods can lead to wrong results. This is due to the fact that these methods do not explicitly preserve the so-called ‘symplectic condition’ (that needs to be satisfied for Hamiltonian systems) at every integration step. In this paper, we look at various methods for integration that preserve the symplectic condition.

Govindan Rangarajan | G. Rangarajan

[1] Govindan Rangarajan,et al. Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics , 1988 .

[2] Christian Pichot,et al. Emulsifier‐free emulsion copolymerization of styrene and butyl acrylate. I. Kinetic studies in the absence of surfactant , 1990 .

[3] C. Scovel,et al. Symplectic integration of Hamiltonian systems , 1990 .

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

[5] J. W. Humberston. Classical mechanics , 1980, Nature.

[6] A. S. Barashkov. Asymptotic forms of solutions of Maxwell's equations , 1991 .

[7] R. Ruth. A Can0nical Integrati0n Technique , 1983, IEEE Transactions on Nuclear Science.

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

[9] J. M. Sanz-Serna,et al. Symplectic integrators for Hamiltonian problems: an overview , 1992, Acta Numerica.

[10] John M. Finn,et al. Lie Series and Invariant Functions for Analytic Symplectic Maps , 1976 .

[11] J. F. Cornwell. Group theory in physics , 1984 .

[12] Govindan Rangarajan. Symplectic completion of symplectic jets , 1996 .

[13] F. Lasagni. Canonical Runge-Kutta methods , 1988 .

[14] Robert D. Skeel,et al. An explicit Runge-Kutta-Nystro¨m method is canonical if and only if its adjoint is explicit , 1992 .