[图书][B] Multiple time scale dynamics
C Kuehn - 2015 - Springer
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 …
in any overview book, several topics are covered only quite briefly. My aim was to focus on …
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations
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 …
evolution equations. The targeted models are envisaged in a wide spectrum of regimes …
Stroboscopic averaging for the nonlinear Schrödinger equation
In this paper, we are concerned with an averaging procedure, namely Stroboscopic
averaging, for highly oscillatory evolution equations posed in a (possibly infinite …
averaging, for highly oscillatory evolution equations posed in a (possibly infinite …
Word series for dynamical systems and their numerical integrators
A Murua, JM Sanz-Serna - Foundations of Computational Mathematics, 2017 - Springer
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 …
some dynamical systems and their discretizations. These series are similar to but more …
Higher-order averaging, formal series and numerical integration III: error bounds
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 …
investigate the properties of numerical integrators may be used to construct high-order …
A technique for studying strong and weak local errors of splitting stochastic integrators
A Alamo, JM Sanz-Serna - SIAM Journal on Numerical Analysis, 2016 - SIAM
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 …
expansions of the strong and weak local errors of splitting algorithms for the integration of …
A formal series approach to averaging: exponentially small error estimates
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 …
numerical integrators may be applied to perform high-order averaging in oscillatory periodic …
Vibrational resonance: a study with high-order word-series averaging
A Murua, JM Sanz-Serna - Applied Mathematics and Nonlinear …, 2016 - sciendo.com
We study a model problem describing vibrational resonance by means of a high-order
averaging technique based on socalled word series. With the technique applied here, the …
averaging technique based on socalled word series. With the technique applied here, the …
The Lie group structure of the Butcher group
G Bogfjellmo, A Schmeding - Foundations of Computational Mathematics, 2017 - Springer
The Butcher group is a powerful tool to analyse integration methods for ordinary differential
equations, in particular Runge–Kutta methods. In the present paper, we complement the …
equations, in particular Runge–Kutta methods. In the present paper, we complement the …
Computing normal forms and formal invariants of dynamical systems by means of word series
A Murua, JM Sanz-Serna - Nonlinear Analysis, 2016 - Elsevier
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 …
dynamical systems to normal form and in the computation of formal invariants of motion in …