Higher order splitting methods with modified integrators for a class of Hamiltonian systems
This provides improved numerical integration for researchers simulating Hamiltonian systems, though the extension is incremental over existing splitting techniques.
The paper presents higher-order splitting methods (up to order τ^8) for Hamiltonian systems, extending the standard Störmer-Verlet method while maintaining real and positive timesteps.
We discuss systematic extensions of the standard (St{ö}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics, with relative accuracy of order $τ^2$ for a timestep of length $τ$, to higher orders in $τ$. We present some splitting schemes, with all intermediate timesteps real and positive, which increase the relative accuracy to order $τ^{N}$ (for N=4, 6, and 8) for a large class of Hamiltonian systems.