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| Author | : Randall J. LeVeque |
| Publisher | : Cambridge University Press |
| Total Pages | : 582 |
| Release | : 2002-08-26 |
| Genre | : Mathematics |
| ISBN | : 1139434187 |
Download Finite Volume Methods for Hyperbolic Problems Book in PDF, ePub and Kindle
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.
| Author | : Serge Alinhac |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 159 |
| Release | : 2009-06-17 |
| Genre | : Mathematics |
| ISBN | : 0387878238 |
Download Hyperbolic Partial Differential Equations Book in PDF, ePub and Kindle
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.
| Author | : Peter D. Lax |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 234 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821835769 |
Download Hyperbolic Partial Differential Equations Book in PDF, ePub and Kindle
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. -- Back cover.
| Author | : V. G. Romanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 160 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 364280781X |
Download Integral Geometry and Inverse Problems for Hyperbolic Equations Book in PDF, ePub and Kindle
There are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solution on the data is retained but it is interpreted differently. It is required that solutions depend continuously only on that data which does not take the solutions out of M.
| Author | : Sylvie Benzoni-Gavage |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1117 |
| Release | : 2008-01-12 |
| Genre | : Mathematics |
| ISBN | : 3540757120 |
Download Hyperbolic Problems: Theory, Numerics, Applications Book in PDF, ePub and Kindle
This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modeling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly.
| Author | : Remi Abgrall |
| Publisher | : Elsevier |
| Total Pages | : 668 |
| Release | : 2016-11-17 |
| Genre | : Mathematics |
| ISBN | : 0444637958 |
Download Handbook of Numerical Methods for Hyperbolic Problems Book in PDF, ePub and Kindle
Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. 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 readily understand their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications Written by leading subject experts in each field who provide breadth and depth of content coverage
| Author | : Carlos Parés |
| Publisher | : Springer Nature |
| Total Pages | : 376 |
| Release | : |
| Genre | : |
| ISBN | : 3031552601 |
Download Hyperbolic Problems: Theory, Numerics, Applications. Volume I Book in PDF, ePub and Kindle
| Author | : Song Jiang |
| Publisher | : World Scientific |
| Total Pages | : 793 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814417092 |
Download Hyperbolic Problems Book in PDF, ePub and Kindle
This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of OC Hyperbolic Partial Differential EquationsOCO. It is aimed at mathematicians, researchers in applied sciences and graduate students."
| Author | : Alfio Quarteroni |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 551 |
| Release | : 2009-02-11 |
| Genre | : Mathematics |
| ISBN | : 3540852689 |
Download Numerical Approximation of Partial Differential Equations Book in PDF, ePub and Kindle
Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).
| Author | : Christian Klingenberg |
| Publisher | : Springer |
| Total Pages | : 714 |
| Release | : 2018-06-27 |
| Genre | : Mathematics |
| ISBN | : 3319915487 |
Download Theory, Numerics and Applications of Hyperbolic Problems II Book in PDF, ePub and Kindle
The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.
