论文信息 - Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods

Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods

SummaryWe consider the question of whether multistep methods inherit in some sense quadratic first integrals possessed by the differential system being integrated. We also investigate whether, in the integration of Hamiltonian systems, multistep methods conserve the symplectic structure of the phase space.

J. M. Sanz-Serna | T. Eirola | T. Eirola | J. Sanz-Serna

[1] V. Arnold. Mathematical Methods of Classical Mechanics , 1974 .

[2] J. M. Sanz-Serna,et al. Runge-kutta schemes for Hamiltonian systems , 1988 .

[3] G. Dahlquist. On One-Leg Multistep Methods , 1983 .

[4] M. Crouzeix,et al. On the equivalence of A-stability and G-stability , 1989 .

[5] G. Dahlquist. Error analysis for a class of methods for stiff non-linear initial value problems , 1976 .

[6] Germund Dahlquist,et al. G-stability is equivalent toA-stability , 1978 .

[7] J. Sanz-Serna,et al. Studies in numerical nonlinear instability III: Augmented Hamiltonian systems , 1987 .

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

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

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

[11] J. G. Verwer,et al. Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation , 1986 .

[12] J. M. Sanz-Serna,et al. A Hamiltonian explicit algorithm with spectral accuracy for the `good' Boussinesq system , 1990 .

[13] W. Watson. Numerical analysis , 1969 .

[14] David B. Gustavson. FASTBUS Software Progress , 1985, IEEE Transactions on Nuclear Science.

[15] J. M. Sanz-Serna,et al. Order conditions for canonical Runge-Kutta schemes , 1991 .

[16] K. Feng. Difference schemes for Hamiltonian formalism and symplectic geometry , 1986 .