102 citations · 183 across the 9 of their papers we have counts for
10 papers
SIMD-vectorized implicit symplectic integrators can outperform explicit ones
Mikel Antoñana, Joseba Makazaga, Ander Murua
The main purpose of this work is to present a SIMD-vectorized implementation of the symplectic 16th-order 8-stage implicit Runge-Kutta integrator based on collocation with Gauss-Le…
Taylor-Fourier approximation
M. P. Calvo, J. Makazaga, A. Murua
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appro…
An implicit symplectic solver for high-precision long term integrations of the Solar System
M. Antoñana, E. Alberdi, J. Makazaga +1
Compared to other symplectic integrators (the Wisdom and Holman map and its higher order generalizations) that also take advantage of the hierarchical nature of the motion of the p…
Global time-renormalization of the gravitational -body problem
M. Antoñana, P. Chartier, J. Makazaga +1
This work considers the {\em gravitational} -body problem and introduces global time-renormalization {\em functions} that allow the efficient numerical integration with fixed ti…
An algorithm based on continuation techniques for minimization problems with highly non-linear equality constraints
Elisabete Alberdi, Mikel Antoñana, Joseba Makazaga +1
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great…
New integration methods for perturbed ODEs based on symplectic implicit Runge-Kutta schemes with application to solar system simulations
Mikel Antoñana, Joseba Makazaga, Ander Murua
We propose a family of integrators, Flow-Composed Implicit Runge-Kutta (FCIRK) methods, for perturbations of nonlinear ordinary differential equations, consisting of the compositio…
Efficient implementation of symplectic implicit Runge-Kutta schemes with simplified Newton iterations
Mikel Antoñana, Joseba Makazaga, Ander Murua
We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK) methods applied to systems of (non-necessarily Hamiltonian) ordinary differential equati…
Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
Mikel Antoñana, Joseba Makazaga, Ander Murua
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. P…
High precision Symplectic Integrators for the Solar System
Ariadna Farrés, Jacques Laskar, Sergio Blanes +3
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…
New families of symplectic splitting methods for numerical integration in dynamical astronomy
Sergio Blanes, Fernando Casas, Ariadna Farres +3
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interes…