Greenspan, D. Completely conservative, covariant numerical methodology. (English) Zbl 0818.70005 Comput. Math. Appl. 29, No. 4, 37-43 (1995). Summary: For a distance dependent potential, Newtonian dynamics is characterized by conservation of energy, linear momentum, and angular momentum. In addition, the basic dynamical equations are covariant, that is, invariant under fundamental coordinate transformations. In this paper, it is shown that related \(N\)-body problems can be solved numerically in such a fashion that, independently of the time step, the identical conservation laws continue to be valid for the approximating difference equations. In addition, the numerical method is covariant. Cited in 15 Documents MSC: 70-08 Computational methods for problems pertaining to mechanics of particles and systems 70F10 \(n\)-body problems 65L12 Finite difference and finite volume methods for ordinary differential equations Keywords:energy conservation; momentum conservation; systems of ordinary differential equations; conservation laws PDF BibTeX XML Cite \textit{D. Greenspan}, Comput. Math. Appl. 29, No. 4, 37--43 (1995; Zbl 0818.70005) Full Text: DOI OpenURL References: [1] Greenspan, D., Arithmetic Applied Mathematics (1980), Pergamon: Pergamon Oxford · Zbl 0443.70003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.