Applied Numerical Analysis & Computational Mathematics最新文献

Exponentially-fitted algorithms are constructed for the derivation of Gauss formulae and implicit Runge-Kutta methods of collocation type making them tuned for oscillatory (or exponential) functions. The weights and the abscissas of these formulae can depend naturally on the frequency ω by the very construction. For twopoints Gauss formulae and two-step Runge-Kutta methods a detailed study of the obtained results is made. In particular the difference in the numerical application of these algorithms with fixed points and/or frequency dependent nodes is analysed. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The task of comparing numerical methods which are designed to solve a particular class of problems is a notoriously difficult and inexact one. However it is important to be able to measure the quality of codes in at least a limited sense so that potential users of the software can have some guidance as to which code they might use to solve their particular problem. There are two important aspects that must be considered when numerical comparisons are contemplated. The first is to classify those codes which can be regarded as being reasonably efficient and so can set a standard against which other codes can be compared. The second is to identify some test problems which will challenge the codes and highlight any weaknesses they may have. In the present paper we consider the first of these two problems and we describe some codes which may be regarded as being amongst the most efficient for solving two-point boundary value problems at the present time. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper proposes a Maxwell's equations finite difference time domain (FDTD) approach for electromagnetic transients in ground electrodes in order to take into account the non linear effects due to soil ionization. A time variable soil resistivity method is used in order to simulate the soil breakdown, without the formulation of an initial hypothesis about the geometrical shape of the ionized zone around the electrodes. The model has been validated by comparing the computed results with available data found in technical literature referred to concentrated earths. Some application examples referred to complex grounding systems are reported to show the computational capability of the proposed model. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

System dynamics is naturally expressed by means of differential equations. Despite their expressive power, they are difficult to reason about and to make decisions upon, given their non-linearity and the important effects that the uncertainty on data may cause. In contrast with traditional numerical simulations that may only provide a likelihood of the results obtained, we propose a constraint reasoning framework that enables safe decision support despite data uncertainty. The approach is illustrated in the tuning of drug design and in an epidemiological study. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A statistical multiplexer is a basic model used in the design and the dimensioning of communication networks. The multiplexer model consists of a finite buffer, to store incoming packets, served by a single server with constant service time, and a more or less complicated arrival process. The aim is to determine the packet loss probability as a function of the capacity of the buffer. An exact analytic approach is unfeasible in real time, and hence we show how techniques from rational approximation theory can be applied to the computation of the packet loss. Since the parameters used in such networks may not produce precise probabilities of interest without having to introduce drastic assumptions, we also carry out a perturbation analysis with respect to these parameters. Using techniques from interval arithmetic, we can deliver sharp bounds for the true uncertainity effect. The latter is very important because the packet loss probability function can be very sensitive to relatively small changes in the network parameters. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we propose a method for the discretization of the parabolic p-Laplacian equation. In particular we use alternately either the backward Euler scheme or the Crank-Nicolson scheme for the time-discretization and the first order Finite Element Method for space-discretization as in [7]. To obtain the numerical solution we have to invert a block Toeplitz matrix with Toeplitz blocks. To this aim we use a Conjugate Gradient (CG) algorithm preconditioned by a block circulant matrix with circulant blocks. A Two-Dimensional Discrete Fast Sine-Cosine Transform (2D-DFSCT) is applied to invert the block circulant matrix with circulant blocks. The experimental results show how the application of the preconditioner reduces the iterations of the CG algorithm of about the 56% –75%. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work, a novel approximation scheme based on a recently developed representation, called the High Dimensional Model Representation (HDMR), is proposed to approximate evolution operators. The approximation is not developed at the operator level, instead the effect of the operator on an arbitrary function is approximated. The purpose of the work is to investigate how HDMR can be applied for the approximation of evolution operator and its efficiency. Although the approximation can be constructed for any order of multivariance, only the constant and univariate components of HDMR are considered in this work. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper an exponentially-fitted multiderivative method is developed for the numerical integration of the Schrödinger equation. We call the method multi-derivative since it uses derivatives of orders two and four. An application to the resonance problem of the radial Schrödinger equation indicates that the new method is more efficient than the Numerov method and other known methods found in the literature. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work aims to apply High Dimensional Model Representation (HDMR) to the sensitivity coefficient determination of the solutions of a multivariate extrema problem. The derivations are made for general functional structure and the illustrative applications are related to structures where the resulting extrema equations are matrix eigenvalue problems. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)