Conservation properties of a time FE method. Part I: time-stepping schemesfor N-body problems

In the present paper one-step implicit integration algorithms for the N-bod y problem are developed. The time-stepping schemes are based on a Petrov-Ga lerkin 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 systema tic implementation of a family of time-stepping schemes. A particular algor ithm is specified by the associated quadrature rule employed for the evalua tion of time integrals. The influence of various standard as well as non-st andard quadrature formulas on algorithmic energy conservation and conservat ion of angular momentum is examined in detail for linear and quadratic time elements. Copyright (C) 2000 John Wiley & Sons, Ltd.