HIGH ACCURACY FREQUENCY DETERMINATION FROM DISCRETE SPECTRA

The problem of determining the characteristics of a sine wave from its discrete spectrum is considered. The nontriviality of the problem is caused basicly by a phenomenon called spectral leakage, that is, by the fact that the spectral envelope of a single sinusoid forms a bell-shaped curve, even in the ideal noiseless case. In the paper a simple and self-contained treatment of spectral leakage is presented and a computationally efficient frequency estimation method is derived, taking into consideration different types of time-domain windows

TOWARDS PRECISION TOOLS FOR ATM NETWORK DESIGN, DIMENSIONING AND MANAGEMENT

It is a critical issue in network dimensioning that the characterization of traffic at the call level should be accurate enough to provide the designer with reliable tools for dimensioning the transmission and switching capacities. Since in B-ISDN the nature of traffic is expected to be very different from traditional telephone traffic with much more complex features, therefore, new methods are needed to provide a satisfactory description. In this paper we present an approach that characterizes the traffic demand at the call level in a refined way, namely, by using a two-parameter description instead of the traditional one-parameter characterization. This approach contributes to the more accurate description of traffic demands at the call level, in order to provide the network designer and manager with precision tools to handle traffic demands and their consequences in dimensioning and related issues, while retaining simplicity, algorithmic feasibility and practical applicability

Stability and Convergence of Product Formulas for Operator Matrices

We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract Cauchy problems and to boundary feedback systems.Comment: to appear in Integral Equations and Operator Theory (ISSN: 1420-8989

On the numerical solution of the three-dimensional advection-diffusion equation

A new approach is proposed for the numerical solution of three-dimensional advection-diffusion equations, which arise, among others, in air pollution modelling. The technique is based on directional operator splitting, which results in one-dimensional advection-diffusion equations. Then upstream-type difference approximations are applied for the first-order derivatives and non-standard difference approximations for the second-order derivatives. This approach leads to significant qualitative improvements in the behaviour of the numerical solutions

Improvement of accuracy of multi-scale models of Li-ion batteries by applying operator splitting techniques

In this work operator splitting techniques have been applied successfully to improve the accuracy of multi-scale Lithium-ion (Li-ion) battery models. A slightly simplified Li-ion battery model is derived, which can be solved on one time scale and multiple time scales. Different operator splitting schemes combined with different approximations are compared with the non-splitted reference solution in terms of stability, accuracy and processor cost. It is shown, that the reverse Strang–Marchuk splitting combined with the implicit scheme to solve the diffusion operator and Newton method to approximate the non-linear source term can improve the accuracy of the commonly applied vertical (sequential) multi-scale models by almost 3 times without considerably increasing the processor cost. © 2016 The Author

The norm convergence of a Magnus expansion method

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.Comment: Rerferee recommendations incorporated. To appear in Central European Journal of Mathematic