Energy Conserving, Arbitrary Order Numerical Solutions of the N-Body Problem.
A Résumé on Interval Runge-Kutta Methods
The paper presents explicit and implicit interval methods of Runge-Kutta type. Such methods introduce the errors of methods. It means that this kind of errors are included in the interval solutions obtained. Applying these methods for solving the initial value problem in floating-point interval arithmetic we can obtain solutions in the form of intervals which contain all possible numerical errors. Numerical examples are presented.
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