130 citations · 506 across the 27 of their papers we have counts for
5 papers · 1 filter
Averaging and computing normal forms with word series algorithms
A. Murua, J. M. Sanz-Serna
In the first part of the present work we consider periodically or quasiperiodically forced systems of the form , where , is a nonres…
Computing normal forms and formal invariants of dynamical systems by means of word series
A. Murua, J. M. Sanz-Serna
We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamilt…
Formal series and numerical integrators: some history and some new techniques
Jesus Maria Sanz-Serna, Ander Murua
This paper provides a brief history of B-series and the associated Butcher group and presents the new theory of word series and extended word series. B-series (Hairer and Wanner 19…
An efficient algorithm based on splitting for the time integration of the Schrödinger equation
S. Blanes, F. Casas, A. Murua
We present a practical algorithm based on symplectic splitting methods to integrate numerically in time the Schrödinger equation. When discretized in space, the Schrödinger equatio…
Word series for dynamical systems and their numerical integrators
Ander Murua, J. M. Sanz-Serna
We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more c…