Global Time-Renormalization of the Gravitational $N$-body Problem

Autor: Ander Murua, Philippe Chartier, Joseba Makazaga, Mikel Antoñana

Publikováno v: SIAM Journal on Applied Dynamical Systems
SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2020, 19 (4), pp.2658-2681. ⟨10.1137/20M1314719⟩
SIAM Journal on Applied Dynamical Systems, 2020, 19 (4), pp.2658-2681. ⟨10.1137/20M1314719⟩

This work considers the {\em gravitational} $N$-body problem and introduces global time-renormalization {\em functions} that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence of the sol

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2087604ebdc57393693909dbdab35573
https://doi.org/10.1137/20m1314719

New high order symplectic integrators via generating functions with its application in many-body problem

Autor: Xiongbiao Tu, Yifa Tang, Ander Murua

Publikováno v: BIT Numerical Mathematics. 60:509-535

A new family of high order one-step symplectic integration schemes for separable Hamiltonian systems with Hamiltonians of the form $$T(p) + U(q)$$ is presented. The new integration methods are defined in terms of an explicitly defined generating func

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::31d7c9eff94d49cd496ccc0b6452958c
https://doi.org/10.1007/s10543-019-00785-0

Continuous changes of variables and the Magnus expansion

Autor: Fernando Casas, Philippe Chartier, Ander Murua

Publikováno v: Journal of Physics Communications
Journal of Physics Communications, IOP Publishing, In press, 3 (9), pp.095014. ⟨10.1088/2399-6528/ab42c1⟩
Journal of Physics Communications, In press, 3 (9), pp.095014. ⟨10.1088/2399-6528/ab42c1⟩
Addi. Archivo Digital para la Docencia y la Investigación
instname
Repositori Universitat Jaume I
Universitat Jaume I
Journal of Physics Communications, inPress, 3 (9), pp.095014. ⟨10.1088/2399-6528/ab42c1⟩

In this paper, we are concerned with a formulation of Magnus and Floquet-Magnus expansions for general nonlinear differential equations. To this aim, we introduce suitable continuous variable transformations generated by operators. As an application

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df7909dd5023966289aee1bb89f6975e
https://hal.inria.fr/hal-02393566/document

Computing normal forms and formal invariants of dynamical systems by means of word series

Autor: Jesús María Sanz-Serna, Ander Murua

Publikováno v: UVaDOC. Repositorio Documental de la Universidad de Valladolid
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We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex numbers rath

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ed638f7eeee0da146face879b62edc5
https://doi.org/10.1016/j.na.2015.10.013

Averaging and Computing Normal Forms with Word Series Algorithms

Autor: Jesús María Sanz-Serna, Ander Murua

Publikováno v: Discrete Mechanics, Geometric Integration and Lie–Butcher Series ISBN: 9783030013967

In the first part of the present work we consider periodically or quasiperiodically forced systems of the form \((d/dt)x = \varepsilon f(x,t \omega )\), where \(\varepsilon \ll 1\), \(\omega \in \mathbb {R}^d\) is a nonresonant vector of frequencies

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::04cf2cb460c988098ddf8011df02b32d
https://doi.org/10.1007/978-3-030-01397-4_4