On higher-order semi-explicit symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems |
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Authors: | Sebastian Reich |
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Institution: | Konrad-Zuse-Zentrum, Heilbronner Stra?e 10, D-10711 Berlin, Germany; e-mail: na.reich@na-net.ornl.gov, DE
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Abstract: | Summary. In this paper we generalize the class of explicit partitioned Runge-Kutta (PRK) methods for separable Hamiltonian systems
to systems with holonomic constraints. For a convenient analysis of such schemes, we first generalize the backward error analysis
for systems in to systems on manifolds embedded in . By applying this analysis to constrained PRK methods, we prove that such methods will, in general, suffer from order reduction
as well-known for higher-index differential-algebraic equations. However, this order reduction can be avoided by a proper
modification of the standard PRK methods. This modification increases the number of projection steps onto the constraint manifold
but leaves the number of force evaluations constant. We also give a numerical comparison of several second, fourth, and sixth
order methods.
Received May 5, 1995 / Revised version received February 7, 1996 |
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Keywords: | Mathematics Subject Classification (1991):65L05 65L20 |
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