Abstract
In the present paper one-step implicit integration algorithms for the N-body problem are developed. The time-stepping schemes are based on a Petrov–Galerkin finite element method applied to the Hamiltonian formulation of the N-body problem. The approach furnishes algorithmic energy conservation in a natural way. The proposed time finite element method facilitates a systematic implementation of a family of time-stepping schemes. A particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals. The influence of various standard as well as non-standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements. Copyright © 2000 John Wiley & Sons, Ltd.
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