Systematic Improvement of Splitting Methods for the Hamilton Equations

Details Systematic Improvement of Splitting Methods for the Hamilton Equations Systematic Improvement of Splitting Methods for the Hamilton Equations

2012-04-18

arxiv.org/abs/1204.4117v1

Mathematics

Numerical Analysis

Accepted contribution The 2012 International Conference of Applied and Engineering Mathematics, London, U.K.,4-6 July 2012. 5

Scientific paper

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.

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