A new class of symplectic integration schemes based on generating functions

@article{Makazaga2009ANC,
  title={A new class of symplectic integration schemes based on generating functions},
  author={Joseba Makazaga and Ander Murua},
  journal={Numerische Mathematik},
  year={2009},
  volume={113},
  pages={631-642}
}
We present a new family of one-step symplectic integration s chemes for Hamiltonian systems of the general forṁ y = J∇H(y) . Such a class of methods contains as particular cases the methods of Miesbach and Pesch [13], and also the family of symplectic Runge-Kutta me thods. As in the case of the methods introduced in [13], the new integrati on methods are constructed by defining a generating function, which automa ically determines a symplectic map. The resulting methods are implicit, and… CONTINUE READING