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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Numerical Analysis
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Progress in Industrial Mathematics at ECMI 2004
ECMI has a brand name in Industrial Mathematics and organises successful biannual conferences. This time, the conference on Industrial Mathematics held in Eindhoven in June 2004 Mathematics focused on Aerospace, Electronic Industry, Chemical Technology, Life Sciences, Materials, Geophysics, Financial Mathematics and Water flow. The majority of the invited talks on these topics can be found in these proceedings. Apart from these lectures, a large number of contributed papers and minisymposium papers are included here. They give an interesting (and impressive) overview of the important place mathematics has achieved in solving all kinds of problems met in industry, and commerce in particular.
Mathematical Models in the Manufacturing of Glass
This volume presents a review of advanced technological problems in the glass industry and of the mathematics involved. It is amazing that such a seemingly small research area is extremely rich and calls for an impressively large variety of mathematical methods, including numerical simulations of considerable complexity. The problems treated here are very typical of the field of glass manufacturing and cover a large spectrum of complementary subjects: injection molding by various techniques, radiative heat transfer in glass, nonisothermal flows and fibre spinning. The book can certainly be useful not only to applied mathematicians, but also to physicists and engineers, who can find in it an overview of the most advanced models and methods.
Report
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Solving Differential Equations by Multistep Initial and Boundary Value Methods
The numerical approximation of solutions of differential equations has been, and continues to be, one of the principal concerns of numerical analysis and is an active area of research. The new generation of parallel computers have provoked a reconsideration of numerical methods. This book aims to generalize classical multistep methods for both initial and boundary value problems; to present a self-contained theory which embraces and generalizes the classical Dahlquist theory; to treat nonclassical problems, such as Hamiltonian problems and the mesh selection; and to select appropriate methods for a general purpose software capable of solving a wide range of problems efficiently, even on parallel computers.
Difference Equations and Inequalities
A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and
From scientific instrument to industrial machine
Architectural stress is the inability of a system design to respond to new market demands. It is an important yet often concealed issue in high tech systems. In From scientific instrument to industrial machine, we look at the phenomenon of architectural stress in embedded systems in the context of a transmission electron microscope system built by FEI Company. Traditionally, transmission electron microscopes are manually operated scientific instruments, but they also have enormous potential for use in industrial applications. However, this new market has quite different characteristics. There are strong demands for cost-effective analysis, accurate and precise measurements, and ease-of-use. ...
Solving Ordinary Differential Equations I
This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.
