Download or read book Mathematical Aspects of Numerical Solution of Hyperbolic Systems written by A.G. Kulikovskii and published by CRC Press. This book was released on 2000-12-21 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics,

Download or read book Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems written by Michael Beals and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases.

Download or read book Finite Volume Methods for Hyperbolic Problems written by Randall J. LeVeque and published by Cambridge University Press. This book was released on 2002-08-26 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Numerical Methods for Conservation Laws written by LEVEQUE and published by Birkhäuser. This book was released on 2013-11-11 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Analytical and Numerical Methods for Wave Propagation in Fluid Media written by K. Murawski and published by World Scientific. This book was released on 2002 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance.Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons.

Download or read book Energy Research Abstracts written by and published by . This book was released on 1983 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for Fluid Dynamics written by Dale R. Durran and published by Springer Science & Business Media. This book was released on 2010-09-14 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean

Download or read book Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws written by Rainer Ansorge and published by Springer Science & Business Media. This book was released on 2012-09-14 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: In January 2012 an Oberwolfach workshop took place on the topic of recent developments in the numerics of partial differential equations. Focus was laid on methods of high order and on applications in Computational Fluid Dynamics. The book covers most of the talks presented at this workshop.

Download or read book Hyperbolic Systems of Conservation Laws written by Philippe G. LeFloch and published by Springer Science & Business Media. This book was released on 2002-07-01 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.

Download or read book Handbook of Numerical Methods for Hyperbolic Problems written by Remi Abgrall and published by Elsevier. This book was released on 2017-01-16 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications - Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage

Download or read book Uncertainty Quantification for Hyperbolic and Kinetic Equations written by Shi Jin and published by Springer. This book was released on 2018-03-20 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Download or read book Mathematical Aspects of Numerical Solution of Hyperbolic Systems written by A.G. Kulikovskii and published by CRC Press. This book was released on 2000-12-21 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena. The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.

Download or read book Analytic Methods for Partial Differential Equations written by G. Evans and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.

Download or read book Research in Progress written by and published by . This book was released on 1991 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Solution of Partial Differential Equations in Science and Engineering written by Leon Lapidus and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of Numerical Solution of PartialDifferential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, evenexhaustive, survey of the subject . . . [It] is unique in that itcovers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic)mode of presentation. Many different computational schemes aredescribed in great detail . . . Numerous practical examples andapplications are described from beginning to the end, often withcalculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages tolucid developments of the methods [for solving partial differentialequations] . . . the writing is very polished and I found it apleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen andEli L. Isaacson. A modern, practical look at numerical analysis,this book guides readers through a broad selection of numericalmethods, implementation, and basic theoretical results, with anemphasis on methods used in scientific computation involvingdifferential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan.Presenting an easily accessible treatment of mathematical methodsfor scientists and engineers, this acclaimed work covers fluidmechanics and calculus of variations as well as more modernmethods-dimensional analysis and scaling, nonlinear wavepropagation, bifurcation, and singular perturbation. 1996(0-471-16513-1) 496 pp.

Download or read book Numerical Methods for Evolutionary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 2008-09-04 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.

Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.