94 citations · 364 across the 34 of their papers we have counts for
7 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…
Adaptive multi-stage integrators for optimal energy conservation in molecular simulations
Mario Fernández-Pendás, Elena Akhmatskaya, J. M. Sanz-Serna
We introduce a new Adaptive Integration Approach (AIA) to be used in a wide range of molecular simulations. Given a simulation problem and a step size, the method automatically cho…
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…
Randomized Hamiltonian Monte Carlo
Nawaf Bou-Rabee, Jesus Maria Sanz-Serna
Tuning the durations of the Hamiltonian flow in Hamiltonian Monte Carlo (also called Hybrid Monte Carlo) (HMC) involves a tradeoff between computational cost and sampling quality,…
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…
Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more
J. M. Sanz-Serna
It is well known that symplectic Runge-Kutta and Partitioned Runge-Kutta methods exactly preserve {\em quadratic} first integrals (invariants of motion) of the system being integra…
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…