@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} }

- Published 2009 in Numerische Mathematik
DOI:10.1007/s00211-009-0243-5

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