Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case

摘要

We follow up on our previous works which presented a possible approach forderiving symplectic schemes for a certain class of highly oscillatoryHamiltonian systems. The approach considers the Hamilton-Jacobi form of theequations of motion, formally homogenizes it and infers an appropriatesymplectic integrator for the original system. In our previous work, the caseof a system exhibiting a single constant fast frequency was considered. Thepresent work successfully extends the approach to systems that have either onevarying fast frequency or several constant frequencies. Some related issues arealso examined.