Talk:Symplectic integrator

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Help with this template Comments: edit – history – watch – refresh Need to add: partitioned Runge-Kutta, Gauss-Legendre, history, connection with generating functions, advantages of symplectic integrators like KAM / Nekhoroshev results, approximate energy preservation, linear error growth. Problems with variable step size. Mention that there are more splitting methods. -- Jitse Niesen (talk) 13:54, 2 August 2007 (UTC)

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Need to add: partitioned Runge-Kutta, Gauss-Legendre, history, connection with generating functions, advantages of symplectic integrators like KAM / Nekhoroshev results, approximate energy preservation, linear error growth. Problems with variable step size. Mention that there are more splitting methods. -- Jitse Niesen (talk) 13:54, 2 August 2007 (UTC)

[edit] A question

It says in the article:

"Symplectic integrators are designed for the numerical solution of Hamilton's equations"

What happens if you try to use a symplectic integrator whose time evolution cannot be derived from a hamiltonian (eg. if the system also includes a dissipative force)? I think this should be mentioned in the article. Ossi 12:48, 25 October 2007 (UTC)

A symplectic integrator is defined in terms of a Hamiltonian, H. If there is no H (as you say, the system cannot be derived from a Hamiltonian) then there is simply no integrator to iterate. Does that make sense? Jcandy 22:16, 27 October 2007 (UTC)