This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

This work is devoted to the numerical simulation of nonlinear Schrödinger and Klein–
Gordon equations. We present a general strategy to construct numerical schemes which are …

We introduce a new methodology to design uniformly accurate methods for oscillatory
evolution equations. The targeted models are envisaged in a wide spectrum of regimes …

In this paper, we are concerned with an averaging procedure, namely Stroboscopic
averaging, for highly oscillatory evolution equations posed in a (possibly infinite …

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 …

The paper considers non-autonomous oscillatory systems of ordinary differential equations
with d≥ 1 non-resonant constant frequencies ω 1,…, ω d. Formal series like those used …

In earlier papers, it has been shown how formal series like those used nowadays to
investigate the properties of numerical integrators may be used to construct high-order …

We present a technique, based on so-called word series, to write down in a systematic way
expansions of the strong and weak local errors of splitting algorithms for the integration of …

The techniques, based on formal series and combinatorics, used nowadays to analyze
numerical integrators may be applied to perform high-order averaging in oscillatory periodic …

The stroboscopic averaging method (SAM) is a technique for the integration of highly
oscillatory differential systems dy/dt= f (y, t) with a single high frequency. The method may be …