pleiades#

diffeqzoo.ivps.pleiades(*, initial_values=((3.0, 3.0, -1.0, -3.0, 2.0, -2.0, 2.0, 3.0, -3.0, 2.0, 0.0, 0.0, -4.0, 4.0), (0.0, 0.0, 0.0, 0.0, 0.0, 1.75, -1.5, 0.0, 0.0, 0.0, -1.25, 1.0, 0.0, 0.0)), time_span=(0.0, 3.0))[source]#

Construct the Pleiades problem in its original, second-order form.

The Pleiades problem from celestial mechanics describes the gravitational interaction(s) of seven stars (the “Pleiades”, or “Seven Sisters”) in a plane. It is a 14-dimensional, second-order differential equation and commonly solved as a 28-dimensional, first-order equation. In in its original, second-order form, it is

\[\ddot u(t) = f(u(t)),\]

with nonlinear dynamics \(f: \mathbb{R}^{14} \rightarrow \mathbb{R}^{14}\).

The Pleiades problem is not stiff. It is a popular benchmark problem because it is not very difficult to solve numerically, but (a) it requires high accuracy in each ODE solver step, and (b) its 14 (or 28) dimensions start to expose those numerical solvers that do not scale well to high dimensions.

A common citation for the Pleiades problem is p. 245 in the book by Hairer et al. (1993):

BibTex for Hairer et al. (1993)

@book{hairer1993solving,
    title={Solving Ordinary Differential equations I, Nonstiff Problems},
    author={Hairer, Ernst and N{\o}rsett, Syvert P and Wanner, Gerhard},
    year={1993},
    publisher={Springer}
    edition={2}
}

Note

If you know a more suitable original reference, please make some noise!