Preface to the Second Edition; Preface to the First Edition; Chapter 1: Background in Linear Algebra; Chapter 2: Discretization of Partial Differential Equations; Chapter 3: Sparse Matrices; Chapter 4: Basic Iterative Methods; Chapter 5: Projection…
Mathematical Modelling and Industrial Mathematics
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We are developing a dual panel breast-dedicated PET system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA-3 ASICs. This paper shows that the coincidence…
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Dieses zweibändige Standardlehrbuch bietet einen umfassenden und aktuellen Überblick über die Numerische Mathematik. Dabei wird besonderer Wert auf solche Vorgehensweisen und Methoden gelegt, die sich durch große Wirksamkeit auszeichnen. Ihr…
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Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the…
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Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady…
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A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R01, then it is unstable. Thus, R0 is a…
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We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed for the…
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Beamforming is critical to the function of most sonar systems. The conspicuous noseleaf and pinna shapes in bats suggest that beamforming mechanisms based on diffraction of the outgoing and incoming ultrasonic waves play a major role in bat…
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Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R0, the contact number and the replacement number R are…
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A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Eulers method for de- terministic differential equations and to have at least an intuitive feel…
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This book deals with infectious diseases - viral, bacterial, protozoan and helminth - in terms of the dynamics of their interaction with host populations. The book combines mathematical models with extensive use of epidemiological and other data.…
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A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae…
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The basic reproductive ratio, R , is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of…
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Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to…
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The Internet has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze…
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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these…
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Heterogeneity in host contact patterns profoundly shapes population-level disease dynamics. Many epidemiological models make simplifying assumptions about the patterns of disease-causing interactions among hosts. In particular, homogeneous-mixing…
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This paper considers the accuracy of projection method approximations to the initialboundary-valueproblemfor the incompressibleNavierStokes equations.The issue of how to correctly specify numerical boundary conditions for these methods has been…
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The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called…
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In this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms input data of the model). The input data are assumed to depend on a finite number of…
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