Symmetric partitioned Runge-Kutta methods for differential equations on Lie groups

Authors:
M. Wandelt;M. GüNther;F. Knechtli;M. Striebel
Affiliations:
Bergische Universität Wuppertal, Fachbereich Mathematik und Naturwissenschaften, D-42119 Wuppertal, Germany;Bergische Universität Wuppertal, Fachbereich Mathematik und Naturwissenschaften, D-42119 Wuppertal, Germany;Bergische Universität Wuppertal, Fachbereich Mathematik und Naturwissenschaften, D-42119 Wuppertal, Germany;Bergische Universität Wuppertal, Fachbereich Mathematik und Naturwissenschaften, D-42119 Wuppertal, Germany
Venue:
Applied Numerical Mathematics
Year:
2012

Citing 2
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proceedings of the on Numerical analysis of hamiltonian differential equations

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Abstract

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 Stormer-Verlet scheme, one of the state-of-the-art schemes used in this subject.