Symplectic Integrator

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This summer I am doing a physics research project involving some computer modeling. One of the main aspects of the simulation that I am doing is using a numerical ODE solver. I originally wrote my own solver using the 4th-order Runge-Kutta method with a variable step size just to get a feel for how these programs work, but in the end I'll be using a different program.

Now I just learned about symplectic ODE solvers the other day and, given the nature of the problem that I'm working on, it seems like one of these integrators would be the way to go (my system is Hamiltonian with constant energy). So, after all of that setup, two questions:

1) Does anyone know of any good symplectic integrators out there? I've searched the internet but the only one I can find (named DiffMan) only runs on UNIX and, unfortunately, I don't have access to a UNIX box on which I could install it. Ideally, I'm looking for a MATLAB program, but I could port it if it's not.
2) I still don't understand all of the ideas behind how these programs use symplectic quantities to solve ODEs, so if anyone knows of a good reference, that would be appreciated as well.


- Jason


A good reference for this is E. Hairer et al., Geometric Numerical Integration, 2nd ed. (Springer, Berlin, 2006).

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