Preserving multiple first integrals by discrete gradients

Details Preserving multiple first integrals by discrete gradients Preserving multiple first integrals by discrete gradients

2010-11-02

arxiv.org/abs/1011.0478v4

Mathematics

Numerical Analysis

17 pages, 3 figures

Scientific paper

We consider systems of ordinary differential equations with known first integrals. The notion of a discrete tangent space is introduced as the orthogonal complement of an arbitrary set of discrete gradients. Integrators which exactly conserve all the first integrals simultaneously are then defined. In both cases we start from an arbitrary method of a prescribed order (say, a Runge-Kutta scheme) and modify it using two approaches: one based on projection and one based one local coordinates. The methods are tested on the Kepler problem.

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