This article reviews the application of various notions from the theory of dynamical systems
to the analysis of numerical approximation of initial value problems over long-time intervals …

This book is an introduction to the theory of shadowing of approximate trajectories in
dynamical systems by exact ones. This is the first book completely devoted to the theory of …

Nonautonomous dynamical systems provide a mathematical framework for temporally
changing phenomena, where the law of evolution varies in time due to seasonal …

We consider semilinear problems of the form u′= Au+ f (u), where A generates an
exponentially decaying compact analytic C 0-semigroup in a Banach space E, f: E α→ E is …

Modified equations for ODEs Page 1 Contemporary Mathematics Volume 172, 1994 Modified
equations for ODEs MP CALVO, A. MURUA AND JM SANZ-SERNA ABSTRACT. We study the …

We derive error bounds for Runge-Kutta time discretizations of semilinear parabolic
equations with nonsmooth initial data. The framework includes reaction-diffusion equations …

Discretizations and Grobman-Hartman Lemma, discretizations and the hierarchy of invariant
manifolds about equilibria are considered. For one-step methods, it is proved that the …

The authors show that for dynamical systems that possess a type of piecewise hyperbolicity
in which there is no decrease in the number of stable modes, the global error in a numerical …

The qualitative behavior of spatially semidiscrete finite element solutions of a semilinear
parabolic problem near an unstable hyperbolic equilibrium \overlineu is studied. It is shown …

The phases of a large class of parabolic partial differential equations with rapid time-periodic
forcing can be separated up to exponential small errors. The originally nonautonomous …