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Families of third and fourth algebraic order trigonometrically fitted symplectic methods for the numerical integration of Hamiltonian systems. (English) Zbl 1196.65192

Summary: The numerical integration of Hamiltonian systems by symplectic and trigonometrically fitted (TF) symplectic method is considered in this work. We construct new trigonometrically fitted symplectic methods of third and fourth order. We apply our new methods as well as other existing methods to the numerical integration of the harmonic oscillator, the 2D harmonic oscillator with an integer frequency ratio and an orbit problem studied by Stiefel and Bettis.

MSC:

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
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