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Systematic Improvement of Splitting Methods for the Hamilton Equations (1204.4117v1)
Published 18 Apr 2012 in math.NA, math-ph, math.MP, and physics.comp-ph
Abstract: We show how the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics (with accuracy of order $\tau2$ 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 $\tau8$, and demonstrate that the method work on a simple anharmonic oscillator.
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