Systematic Improvement of Splitting Methods for the Hamilton Equations
  We show how the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics (with accuracy of order $\tau^2$ for a timestep of length $\tau$) can be improved in a systematic manner without using the composition method. We give the explicit expressions which increase the accuracy to order $\tau^8$, and demonstrate that the method work on a simple anharmonic oscillator. 
Asif Mushtaq, Anne Kv{\ae}rn{\o}, and K{\aa}re Olaussen
math.NA math-ph math.MP physics.comp-ph