Discrete gradient algorithms of high order for one-dimensional systems

Details Discrete gradient algorithms of high order for one-dimensional systems Discrete gradient algorithms of high order for one-dimensional systems

2010-08-23

arxiv.org/abs/1008.3895v1

Physics

Computational Physics

22 pages, 9 figures

Scientific paper

We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories in the phase space. The accuracy of our integrators is higher by several orders of magnitude as compared with the standard discrete gradient scheme (modified midpoint rule) and, what is more, our schemes have very high accuracy even for large time steps.

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