2021/03/23 by Mikel Antoñana, Antoñana, Mikel, Philippe Chartier +3
Computer Science · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Applied mathematics #Classical mechanics #Convergence (economics) #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #Geology #Geometry #Geophysics and Gravity Measurements #Gravitation #Mathematical analysis #Mathematics #Midpoint #Numerical Analysis (math.NA) #Numerical methods for differential equations #Physics #Power series #Series (stratigraphy) #Simple (philosophy) #Work (physics) #cs.NA #math.DS #math.NA
paper · pdf · doi:10.48550/arxiv.2103.12839
27 pages, 5 figures
openalex publication_date 2021/03/23 · arxiv created 2021/07/21 · arxiv updated 2021/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As a follow-up of a previous work of the authors, this work considers \em uniform global time-renormalization functions for the \em gravitational N-body problem. It improves on the estimates of the radii of convergence obtained therein by using a completely different technique, both for the solution to the original equations and for the solution of the renormalized ones. The aforementioned technique which the new estimates are built upon is known as \em majorants and allows for an easy application of simple operations on power series. The new radii of convergence so-obtained are approximately doubled with respect to our previous estimates. In addition, we show that \em majorants may also be constructed to estimate the local error of the \em implicit midpoint rule (and similarly for Runge-Kutta methods) when applied to the time-renormalized N-body equations and illustrate the interest of our results for numerical simulations of the solar system.