Systematic Improvement of Splitting Methods for the Hamilton Equations

Abstract

We show how the standard (St{ö}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.

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

References in corpus (1)

• Splitting and composition methods in the numerical integration of differential equations

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