This book provides an approach to the study of perturbation and discretization effects on the
long-time behavior of dynamical and control systems. It analyzes the impact of time and …

The understanding of adaptive algorithms for stochastic differential equations (SDEs) is an
open area, where many issues related to both convergence and stability (long-time …

This paper presents a comparison between two abstract frameworks in which one can treat
multi-valued semiflows and their asymptotic behaviour. We compare the theory developed …

Popular methods for identifying transition paths between energy minima, such as the
nudged elastic band and string methods, typically do not incorporate potential energy …

We introduce a variable timestep** procedure using local error control for the pathwise
(strong) numerical integration of a system of stochastic differential equations forced by a …

In this work we study the problem of step size selection for numerical schemes, which
guarantees that the numerical solution presents the same qualitative behavior as the …

We prove convergence results on finite time intervals, as the user-defined tolerance τ→ 0,
for a class of adaptive timestep** ODE solvers that includes the ode23 routine supplied in …

The standard upper and lower semicontinuity results for discretized attractors [22],[13],[5] are
generalized for discretizations with variable stepsize. Several examples demonstrate that …

The asymptotic behavior of continuous dissipative systems and dissipative numerical
integrators with fixed time-step** can be fully investigated by a Lyapunov-type theorem on …

A nonautonomous or cocycle dynamical system that is driven by an autonomous dynamical
system acting on a compact metric space is assumed to have a uniform pullback attractor. It …