We follow up on our previous works [11, 12] which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of motion, formally homogenizes it and infers an appropriate symplectic integrator for the original system. In [11, 12] the case of a system exhibiting a single constant fast frequency was considered. The present work successfully extends the approach to systems that have either one varying fast frequency or several constant frequencies. Some related issues are also examined.
We also refer to REF for a generalization of this method to systems that have either one varying fast frequency or several constant frequencies.
Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case
arXiv: Numerical Analysis
Mathematics