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We present a new mixed variable symplectic (MVS) integrator for planetary systems, that fully resolve close encounters. The method is based on a time regularisation that allows keeping the stability properties of the symplectic integrators,…

Earth and Planetary Astrophysics · Physics 2019-07-31 Antoine C. Petit , Jacques Laskar , Gwenaël Boué , Mickaël Gastineau

In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady non-linear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes.…

Numerical Analysis · Mathematics 2018-05-29 Daniele A. Di Pietro , Jérôme Droniou

Analytical $f(R)$-gravity models introduce Yukawa-like corrections to the Newtonian potential in the weak field limit. These models can explain the dynamics of galaxies and cluster of galaxies without requiring dark matter. To test the…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-20 I. De Martino , M. De Laurentis , F. Atrio-Barandela , S. Capozziello

The modeling of many phenomena in various fields such as mathematics, physics, chemistry, engineering, biology, and astronomy is done by the nonlinear partial differential equations (PDE). The hyperbolic telegraph equation is one of them,…

Numerical Analysis · Mathematics 2020-10-07 Ahmed K. Al-Jaberi , Ehsan M. Hameed , Mohammed S. Abdul-Wahab

In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…

Instrumentation and Methods for Astrophysics · Physics 2009-04-02 O. T. Kosmas , D. S. Vlachos

We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the…

Computational Physics · Physics 2019-05-07 Carlo Danieli , Bertin Many Manda , Mithun Thudiyangal , Charalampos Skokos

Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new…

Numerical Analysis · Mathematics 2026-02-20 Songchen Tan , Oscar Smith , Christopher Rackauckas

The cosmographic approach is adopted to determine the spatial curvature (i.e., $\Omega_K$) combining the latest released cosmic chronometers data (CC), the Pantheon sample of type Ia supernovae observations, and the baryon acoustic…

Cosmology and Nongalactic Astrophysics · Physics 2020-01-08 En-Kun Li , Minghui Du , Lixin Xu

In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…

Numerical Analysis · Mathematics 2025-02-13 M. P. Calvo , J. Makazaga , A. Murua

We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…

Numerical Analysis · Mathematics 2019-11-12 Pouria Behnoudfar , Quanling Deng , Victor M. Calo

Extrasolar planetary systems commonly exhibit planets on eccentric orbits, with many systems located near or within mean-motion resonances, showcasing a wide diversity of orbital architectures. Such complex systems challenge traditional…

Earth and Planetary Astrophysics · Physics 2025-07-25 Aya Alnajjarine , Federico Mogavero , Jacques Laskar

Fast and accurate integration of geodesics in Kerr spacetimes is an important tool in modeling the orbits of stars and the transport of radiation in the vicinities of black holes. Most existing integration algorithms employ Boyer-Lindquist…

High Energy Astrophysical Phenomena · Physics 2018-11-07 Chi-kwan Chan , Lia Medeiros , Feryal Ozel , Dimitrios Psaltis

Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims.…

Earth and Planetary Astrophysics · Physics 2022-01-12 Piotr A. Dybczyński , Sławomir Breiter

The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…

Space Physics · Physics 2010-02-17 Valeriy V. Petrov

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the…

Numerical Analysis · Mathematics 2016-09-06 Pauline Lafitte , Ward Melis , Giovanni Samaey

We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…

Dynamical Systems · Mathematics 2024-07-26 Robert Szczelina , Piotr Zgliczyński

We present a new approach to study galaxy evolution in a cosmological context. We combine cosmological merger trees and semi-analytic models of galaxy formation to provide the initial conditions for multi-merger hydrodynamic simulations. In…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-11 Benjamin P. Moster , Andrea V. Macciò , Rachel S. Somerville

GYOTO, a general relativistic ray-tracing code, is presented. It aims at computing images of astronomical bodies in the vicinity of compact objects, as well as trajectories of massive bodies in relativistic environments. This code is…

General Relativity and Quantum Cosmology · Physics 2012-03-15 Frederic H. Vincent , Thibaut Paumard , Eric Gourgoulhon , Guy Perrin

In 2023, the 12th edition of Global Trajectory Competition was organised around the problem referred to as "Sustainable Asteroid Mining". This paper reports the developments that led to the solution proposed by ESA's Advanced Concepts Team.…