by Qun Ma In post-genomic computational biology and bioinformatics, long simulations of the dynamics of molecular systems, particularly biological molecules such as proteins and DNA, require advances in time stepping computational methods. The most severe problem of these algorithms is instability. The objective of this dissertation is to present original work in constructing multiscale multipl...

Nygren, J. 2016. Input-Output Stability Analysis of Networked Control Systems. Uppsala Dissertations from the Faculty of Science and Technology 119. 147 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9452-0. The main focus of the thesis is to derive stability criteria for networked control system (NCS) models featuring imperfections such as time-varying and constant delays, quanti...

Although many mathematicians have searched on the fractional calculus since many years ago, but its application in engineering, especially in modeling and control, does not have many antecedents. Since there are much freedom in choosing the order of differentiator and integrator in fractional calculus, it is possible to model the physical systems accurately. This paper deals with time-domain id...

Introduction: The leaky integrator is a key subsystem in pulse-mode artificial neuron implementations [1]. In most implementations reported to date this function has been implemented with the explicit use of integrated capacitors and with fixed time constants. More recently it has been noted that mimicking real biological systems is better accomplished if the integrator time constants are adapt...

Nonlinear wave motion in dispersive media is solved numerically. The model applies to laser propagation in a relativistic plasma. The latter causes, besides dispersion, nonlinear effects due to relativistic mass variation in the presence of strong laser pulses. A new variant of the Gautschi–type integrator for reducing the number of time steps is proposed as a fast solver for such nonlinear wav...

For the solution of one dimensional cubic nonlinear Schrödinger equation on torus, we propose and analyze a fully discrete low-regularity integrator. The considered scheme is explicit. Its implementation relies fast Fourier transform with complexity $${\mathcal {O}}(N\log N)$$ operations per time step, where N denotes degrees freedom in spatial discretization. We prove that new provides an {O}}...

A number of numerical algorithms have been developed for various special classes of DAEs. This paper describes a new variable step size, constraint preserving integrator for general nonlinear fully implicit higher index DAEs. Numerical implementation issues are discussed. Numerical examples illustrate the effectiveness of the new method.

We study nonlinear continuous-time consensus protocols for networks of agents, described by a single-integrator model. The network topology is fixed and connected, but the communication and measurement delays may present. Using the absolute stability methods, we obtain effective condition for convergence of such consensus protocols, given the couplings to satisfy sector inequalities.