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

Efficient implementation of symplectic implicit Runge-Kutta schemes with simplified Newton iterations

Autor: Mikel Antoñana, Joseba Makazaga, Ander Murua

Publikováno v: Addi. Archivo Digital para la Docencia y la Investigación
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We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK) methods applied to systems of (non-necessarily Hamiltonian) ordinary differential equations by means of Newton-like iterations. We pay particular attention to

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0e9cd411c5608f832e7bf8a9826e36d3
http://hdl.handle.net/10810/21073

Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes

Autor: Joseba Makazaga, Mikel Antoñana, Ander Murua

Publikováno v: Addi. Archivo Digital para la Docencia y la Investigación
instname

We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating point arith

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7f3ecf71f7ed8ac9afc8038503f85c99

New Runge–Kutta Based Schemes for ODEs with Cheap Global Error Estimation

Autor: Joseba Makazaga, Ander Murua

Publikováno v: BIT Numerical Mathematics. 43:595-610

We present a particular 5th order one-step integrator for ODEs that provides an estimation of the global error. It's based on the class of one-step integrator for ODEs of Murua and Makazaga considered as a generalization of the globally embedded RK m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ffd0e0cfea87738c546e15ab1dbefec8
https://doi.org/10.1023/b:bitn.0000007056.32638.fb

High precision symplectic integrators for the Solar System

Autor: Jacques Laskar, Ariadna Farrés, Ander Murua, Joseba Makazaga, Sergio Blanes, Fernando Casas

Publikováno v: Celestial Mechanics and Dynamical Astronomy
Celestial Mechanics and Dynamical Astronomy, Springer Verlag, 2013, 116 (2), pp.141-174. ⟨10.1007/s10569-013-9479-6⟩
Celestial Mechanics and Dynamical Astronomy, 2013, 116 (2), pp.141-174. ⟨10.1007/s10569-013-9479-6⟩
Repositori Universitat Jaume I
Universitat Jaume I
RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname

Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. These comparisons are made

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eeeb40640a3fc46dfaf705001fc2f72d
https://hal.archives-ouvertes.fr/hal-02526374