Author: Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 820
Book Description
Author: Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes)
Author: Heinrich G W BegehrPublisher: World Scientific
ISBN: 9814485233
Category : Mathematics
Languages : en
Pages : 1557
Book Description
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
The Asian Journal of Mathematics
Author: Mathematical Reviews
Author: Hyperbolic Partial Differential Equations
Author: Serge AlinhacPublisher: Springer Science & Business Media
ISBN: 0387878238
Category : Mathematics
Languages : en
Pages : 159
Book Description
This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.
Numerical Methods for Conservation Laws
Author: LEVEQUEPublisher: Birkhäuser
ISBN: 3034851162
Category : Science
Languages : en
Pages : 221
Book Description
These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
Finite Volume Methods for Hyperbolic Problems
Author: Randall J. LeVequePublisher: Cambridge University Press
ISBN: 1139434187
Category : Mathematics
Languages : en
Pages : 582
Book Description
This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Mathematical Aspects of Modelling Oscillations and Wake Waves in Plasma
Author: E.V. ChizhonkovPublisher: CRC Press
ISBN: 1000012190
Category : Science
Languages : en
Pages : 175
Book Description
This book is devoted to research in the actual field of mathematical modeling in modern problems of plasma physics associated with vibrations and wake waves excited by a short high-power laser pulse. The author explores the hydrodynamic model of the wake wave in detail and from different points of view, within the framework of its regular propagation, a development suitable for accelerating electrons, and the final tipping effect resulting in unregulated energy transfer to plasma particles. Key selling features: Presents research directly related to the propagation of super-power short laser pulses (subject of the 2018 Nobel Prize in Physics). Presents mathematical modeling of plasma physics associated with vibrations and wake waves excited by a short high-power laser pulse. Includes studies of large-amplitude plasma oscillations. Most of the presented results are of original nature and have not appeared in the domestic and foreign scientific literature Written at a level accessible for researchers, academia, and engineers.
Kinetic Formulation of Conservation Laws
Author: B. PerthamePublisher: Oxford University Press
ISBN: 9780198509134
Category : Language Arts & Disciplines
Languages : en
Pages : 212
Book Description
Written by a well-known expert in the field, the focus of this book is on an innovative mathematical and numerical theory which applies to classical models of physics such as shock waves and balance laws. The text is based on early works in common with P.L. Lions (field medalist).
Nonlinear Problems of Elasticity
Author: Stuart AntmanPublisher: Springer Science & Business Media
ISBN: 1475741472
Category : Mathematics
Languages : en
Pages : 762
Book Description
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.