5 citations · 16 across the 7 of their papers we have counts for
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Geometrization of symplecticity conditions for implicit schemes
Hugo Jiménez-Pérez
In this note we give simple symplecticity conditions for implicit schemes in the linear case. We consider implicit maps on generic symplectic manifold and we introduce the concept…
Towards exact symplectic integrators from Liouvillian forms
Hugo Jiménez-Pérez
In this article we introduce a low order implicit symplectic integrator designed to follow the Hamiltonian flow as close as possible. This integrator is obtained by the method of L…
New insights on numerical error in symplectic integration
Hugo Jiménez-Pérez, Jean-Pierre Vilotte, Barbara Romanowicz
We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the c…
On the Poincaré's generating function and the symplectic mid-point rule
Hugo Jiménez-Pérez, Jean-Pierre Vilotte, Barbara Romanowicz
The use of Liouvillian forms to obtain symplectic maps for constructing numerical integrators is a natural alternative to the method of generating functions, and provides a deeper…
Symplectic maps: from generating functions to Liouvillian forms
Hugo Jiménez-Pérez
In this article we introduce a new method for constructing implicit symplectic maps using special symplectic manifolds and Liouvillian forms. This method extends, in a natural way,…