Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie Groups

Details Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie Groups Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie Groups

2011-09-14

arxiv.org/abs/1109.3030v1

Physics

High Energy Physics

High Energy Physics - Lattice

18 pages, 2 figures, 2 tables

Scientific paper

In this paper, we develop a higher order symmetric partitioned Runge-Kutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned Runge-Kutta methods on Lie groups of arbitrary order. As symmetry is not met for higher orders, we generalize the method to a symmetric partitioned Runge-Kutta (SPRK) scheme. Furthermore, we derive a set of coefficients for convergence order 4. The SPRK integration method can be used, for example, in simulations of quantum field theories. Finally, we compare the new SPRK scheme numerically with the St\"ormer-Verlet scheme, one of the state-of-the-art schemes used in this subject.

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