This book is a substantially revised and expanded edition reflecting major developments in
stochastic numerics since the 1st edition [314] was published in 2004. The new topics …

We use an optimal control protocol to cool one mode of the center-of-mass motion of an
optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force …

Some new stochastic Runge–Kutta (SRK) methods for the strong approximation of solutions
of stochastic differential equations (SDEs) with improved efficiency are introduced. Their …

Nanomechanical resonators are widely operated as force and mass sensors with
sensitivities in the zepto-Newton (10–21) and yocto-gram (10–24) regime, respectively …

Real-world text applications often involve composing a wide range of text control operations,
such as editing the text wrt an attribute, manipulating keywords and structure, and …

Inspired by recent advances in the theory of modified differential equations, we propose a
new methodology for constructing numerical integrators with high weak order for the time …

Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von
Neumann entropy, therefore representing examples of pure steady states. Nonequilibrium …

Backward error analysis is a powerful tool in order to detect the long-term conservative
behavior of numerical methods. In this work, we present a long-term analysis of symplectic …

Traditional explicit schemes such as the Euler-Maruyama, Milstein and stochastic Runge-
Kutta methods, in general, result in strong and weak divergence when solving stochastic …

This study concerns the approximation of some stochastic integrals used in the strong
second-order methods for several classes of stochastic differential equations. An explicit …