13 research outputs found
High order explicit symplectic integrators for the Discrete Non Linear Schr\"odinger equation
We propose a family of reliable symplectic integrators adapted to the
Discrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H.
Yoshida, Construction of higher order symplectic integrators, Physics Letters
A, 150, 5,6,7, (1990), pp. 262.) we can construct high order numerical schemes,
that result to be explicit methods and thus very fast. The performances of the
integrators are discussed, studied as functions of the integration time step
and compared with some non symplectic methods
On the use of the MEGNO indicator with the global symplectic integrator
To distinguish between regular and chaotic orbits in Hamiltonian systems, the
Global Symplectic Integrator (GSI) has been introduced, based on the symplectic
integration of both Hamiltonian equations of motion and variational equations.
In the present contribution, we show how to compute efficiently the MEGNO
indicator jointly with the GSI. Moreover, we discuss the choice of symplectic
integrator, in fact we point out that a particular attention has to be paid to
the structure of the Hamiltonian system associated to the variational
equations. The performances of our method is illustrated through the study of
the Arnold diffusion problem
Principles of Feature Modeling
QC 20190926</p