102 citations · 183 across the 9 of their papers we have counts for
7 papers · 1 filter
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 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…
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…