Systematic Improvement of Splitting Methods for the Hamilton Equations
This provides a method to enhance numerical integration for Hamiltonian systems, relevant for computational physics and molecular dynamics.
The authors present a systematic approach to improve the accuracy of the standard Störmer-Verlet splitting method for Hamiltonian mechanics, achieving up to order τ^8 accuracy without composition, and demonstrate it on an anharmonic oscillator.
We show how the standard (St{ö}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics (with accuracy of order $τ^2$ for a timestep of length $τ$) can be improved in a systematic manner without using the composition method. We give the explicit expressions which increase the accuracy to order $τ^8$, and demonstrate that the method work on a simple anharmonic oscillator.