4 papers · 1 filter
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…