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Stub symplectic integrator, just a list of basic references so far, redirecting aslo multisymplectic integrator.
I have added a minimum of an idea and a minimum of cross-links.
(That Wikipedia entry linked to is crazy…)
I am going to correct this, the ad hoc idea section is rather grossly missing the point. It is not about the specific kind of natural Hamiltonians, on the contrary, the method is applicable much further and it generalizes even to the multisymplectic geometry, as the titles of the quoted references say. It is rather the point that the discretization is made in such a way that the conservation laws/symplectic structure are observed in the discretization scheme, resulting in much better long-time behaviour than that of the generic discretization scheme. On the other hand, there are many numerical discretization schemes for Hamiltonian systems (including for the quoted natural ones) which are NOT symplectic integrators, in fact most of them are not.
A symplectic integrator is a numerical discretization scheme for solving Hamilton’s equations which takes into account the symplectic structure and, in particular, the conservation laws, at the discretization level, thus resulting in better long-time behaviour of numerical solutions than that of generic discretization schemes. There are analogues for classical field theory, which take into account the resulting multisymplectic structure.
I added redirect Jerrold E. Marsden to related item Jerrold Marsden. Most of published references he signes with this signature. I kindly ask people who create entries for math authors to always create a redirect for the default name which appears in the publications, so that we can link references to authors without shortening official publication author names (to name few examples, we had entries Dan Freed and Jim Stasheff which at some point, and before my intervention, did not correctly link to, incomparably more frequently found in print, Daniel Freed and James Stasheff). I am not in favour of writing all possible aliases, one can use the form with bar to link strange versions but at least the standard publication name should be present, in my opinion.
I would add that the theory of (multi)symplectic integrators is quite an elaborate theory; namely much of the standard aparatus of symplectic geometry is reflected at the discrete level, including Legendre transformation, Noether charges and so on…Is there some difference analogue of a synthetic topos lurking there ;) ?
Added links to keywords.
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