Completely conservative, covariant numerical methodology. (English) Zbl 0818.70005

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.


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
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[1] Greenspan, D., Arithmetic Applied Mathematics (1980), Pergamon: Pergamon Oxford · Zbl 0443.70003
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