A new class of symplectic integration schemes based on generating functions
| Autor: | Ander Murua, Joseba Makazaga |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Hamiltonian mechanics
Pure mathematics Applied Mathematics Mathematical analysis Symplectic representation Computational Mathematics symbols.namesake symbols Symplectic integrator Nabla symbol Symplectomorphism Mathematics::Symplectic Geometry Moment map Symplectic manifold Symplectic geometry Mathematics |
| Zdroj: | Numerische Mathematik. 113:631-642 |
| ISSN: | 0945-3245 0029-599X |
| DOI: | 10.1007/s00211-009-0243-5 |
| Popis: | We present a new family of one-step symplectic integration schemes for Hamiltonian systems of the general form $${\dot y=J^{-1}\nabla H(y)^T}$$. Such a class of methods contains as particular cases the methods of Miesbach and Pesch (Numer Math 61:501–521, 1992), and also the family of symplectic Runge-Kutta methods. As in the case of the methods introduced in Miesbach and Pesch (Numer Math 61:501–521, 1992), the new integration methods are constructed by defining a generating function, which automatically determines a symplectic map. The resulting methods are implicit, and require the evaluation of the gradient of the Hamiltonian function as well as the Hessian times a vector. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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