Fourier interpolation method in phase space of Hamiltonian systems

Sasa, Narimasa  

The validity of the interpolation method in the phase space is investigated in symplectic time integration of Hamiltonian systems. Theoretically, we show that the orbit of the interpolated point in the phase space coincides with the true orbit defined by Hamilton's equations of motion under restricted conditions using the discrete Fourier interpolation method. Even under general conditions, the interpolated point in the phase space evolves close to the true orbit. We conduct numerical simulations to demonstrate that our interpolation method, which approximates the true orbit, has sufficient numerical accuracy under general conditions.