Higher order splitting methods with modified integrators for a class of Hamiltonian systems

Abstract

We discuss systematic extensions of the standard (St{ö}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics, with relative accuracy of order ${\tau }^2$ for a timestep of length $\tau$, to higher orders in $\tau$. We present some splitting schemes, with all intermediate timesteps real and positive, which increase the relative accuracy to order ${\tau }^N$ (for N=4, 6, and 8) for a large class of Hamiltonian systems.

22 pages, 7 figures

References in corpus (2)

• Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
• Fermi, Pasta, Ulam and a mysterious lady

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