130 citations · 506 across the 27 of their papers we have counts for
28 papers
Error bounds for splitting methods in unitary problems
Fernando Casas, Ander Murua
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decompos…
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…
Splitting Methods for differential equations
Sergio Blanes, Fernando Casas, Ander Murua
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve t…
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…
Majorant series for the -body problem
Mikel Antoñana, Philippe Chartier, Ander Murua
As a follow-up of a previous work of the authors, this work considers {\em uniform global time-renormalization functions} for the {\em gravitational} -body problem. It improves…