Geometrization of symplecticity conditions for implicit schemes
This work offers theoretical foundations for symplectic integrators, relevant to researchers in geometric numerical integration and symplectic geometry.
The paper derives simple symplecticity conditions for implicit numerical schemes in the linear case and generalizes them to symplectic manifolds via the concept of consistent implicit maps, providing a preliminary geometric interpretation.
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 of consistent implicit maps, to generalize the symplecticity conditions to symplectic manifolds. Additionally, we give a preliminary geometrical interpretation of those conditions.