Analysis And Numerics For Conservation Laws
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Numerical Methods For Conservation Laws
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Author : LEVEQUE
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Numerical Methods For Conservation Laws written by LEVEQUE and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
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.
Analysis And Numerics For Conservation Laws
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Author : Gerald Warnecke
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-05
Analysis And Numerics For Conservation Laws written by Gerald Warnecke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-05 with Mathematics categories.
Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally. The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In ?ows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that in?uence the stability of the wings as well as fuel consumption in ?ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for e?ciency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial di?erential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scienti?c progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua, partial di?erential equationsareamajor?eldofresearchinmathematics. Asubstantialportionof mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more spacedimensionsstillposeoneofthemainchallengestomodernmathematics.
Numerical Approximation Of Hyperbolic Systems Of Conservation Laws
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Author : Edwige Godlewski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Numerical Approximation Of Hyperbolic Systems Of Conservation Laws written by Edwige Godlewski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.
This work is devoted to the theory and approximation of nonlinear hyper bolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors, and we shall make frequent references to Godlewski and Raviart (1991) (hereafter noted G. R. ), though the present volume can be read independently. This earlier publication, apart from a first chap ter, especially covered the scalar case. Thus, we shall detail here neither the mathematical theory of multidimensional scalar conservation laws nor their approximation in the one-dimensional case by finite-difference con servative schemes, both of which were treated in G. R. , but we shall mostly consider systems. The theory for systems is in fact much more difficult and not at all completed. This explains why we shall mainly concentrate on some theoretical aspects that are needed in the applications, such as the solution of the Riemann problem, with occasional insights into more sophisticated problems. The present book is divided into six chapters, including an introductory chapter. For the reader's convenience, we shall resume in this Introduction the notions that are necessary for a self-sufficient understanding of this book -the main definitions of hyperbolicity, weak solutions, and entropy present the practical examples that will be thoroughly developed in the following chapters, and recall the main results concerning the scalar case.
Numerical Methods For Conservation Laws
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Author : Jan S. Hesthaven
language : en
Publisher: SIAM
Release Date : 2018-01-30
Numerical Methods For Conservation Laws written by Jan S. Hesthaven and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Science categories.
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms: offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material are available online at www.siam.org/books/cs18.
Numerical Partial Differential Equations
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Author : J.W. Thomas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Numerical Partial Differential Equations written by J.W. Thomas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation. Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient. This is the second volume of a two-part book.
Front Tracking For Hyperbolic Conservation Laws
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Author : Helge Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-08
Front Tracking For Hyperbolic Conservation Laws written by Helge Holden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-08 with Mathematics categories.
Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.
Analytical And Numerical Methods For Differential Equations And Applications
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Author : Jesus Martin-Vaquero
language : en
Publisher: Frontiers Media SA
Release Date : 2021-10-29
Analytical And Numerical Methods For Differential Equations And Applications written by Jesus Martin-Vaquero and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-29 with Science categories.
Kinetic Formulation Of Conservation Laws
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Author : B. Perthame
language : en
Publisher: Oxford University Press
Release Date : 2002-12-05
Kinetic Formulation Of Conservation Laws written by B. Perthame and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-05 with Language Arts & Disciplines categories.
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).
Numerical Analysis Using R
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Author : Graham W. Griffiths
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-26
Numerical Analysis Using R written by Graham W. Griffiths and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Computers categories.
This book presents the latest numerical solutions to initial value problems and boundary valu problems described by ODES (Ordinary differencial equations) and PDEs (partiral differential equations). The primary focus in numerical solutions to initial value problems (IVPs) and boundary value problems (BVPs).
Analytical And Numerical Approaches To Asymptotic Problems In Analysis
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Author : O. Axelsson
language : en
Publisher: Elsevier
Release Date : 2010-07-03
Analytical And Numerical Approaches To Asymptotic Problems In Analysis written by O. Axelsson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-03 with Mathematics categories.
Analytical and Numerical Approaches to Asymptotic Problems in Analysis