Book Description
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Customer Reviews:
The most reliable source of solvable nonlinear PDEs.......2007-01-17
It is a very rare occasion when a nonlinear partial differential equation admits an exact solution. Such cases are of the utmost importance as they enable the full and most detailed analysis of the problem concerned. This reference book contains the most extended list of nonlinear PDEs known to be solvable to date and gives not only their exact solutions but also solution methods.
It is a really good book.
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Numerical Methods For Differential Equations: Fundamental Concepts For Scientific & Engineering Applications
Michael A. Celia , and
William G. Gray
Manufacturer: Prentice Hall
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Binding: Paperback
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ASIN: 0136269613 |
Book Description
From the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering:
* "The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject . . . [It] is unique in that it covers 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 are described in great detail . . . Numerous practical examples and applications are described from beginning to the end, often with calculated results given."-Mathematics of Computing.
* "This volume . . . devotes its considerable number of pages to lucid developments of the methods [for solving partial differential equations] . . . the writing is very polished and I found it a pleasure to read!"-Mathematics of Computation
Of related interest . . .NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen and Eli L. Isaacson. A modern, practical look at numerical analysis, this book guides readers through a broad selection of numerical methods, implementation, and basic theoretical results, with an emphasis on methods used in scientific computation involving differential equations. 1997 (0-471-55266-6) 512 pp.
APPLIED MATHEMATICS Second Edition, J. David Logan. Presenting an easily accessible treatment of mathematical methods for scientists and engineers, this acclaimed work covers fluid mechanics and calculus of variations as well as more modern methods-dimensional analysis and scaling, nonlinear wave propagation, bifurcation, and singular perturbation. 1996 (0-471-16513-1) 496 pp.
Customer Reviews:
may be useful but ..........2005-05-06
In my opinion,in order to make use of this book you have to know the subject better then Lapidus or Pinder, maybe then it may start to make sense. As for me, nothing special is included, which you can not find in any other book on partial differential equations, yet the text is not well presented. You get lost in the backward and forward jupms. The good thing is the richness of the subjects embedded to the book, but index page can give you hard times finding those.
Este libro tiene muy buena base..........2001-04-14
Me ayudó mucho en lo que necesitaba aprender y fue muy fácil entenderlo...
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Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics (Chapman & Hall/Crc Applied Mathematics and Nonlinear Science)
Victor A. Galaktionov , and
Sergey R. Svirshchevskii
Manufacturer: Chapman & Hall/CRC
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Binding: Hardcover
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ASIN: 1584886633 |
Book Description
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
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Verification of Computer Codes in Computational Science and Engineering
Patrick Knupp
Manufacturer: Chapman & Hall/CRC
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Verification and Validation in Computational Science and Engineering
ASIN: 1584882646 |
Book Description
How can one be assured that computer codes that solve differential equations are correct? Standard practice using benchmark testing no longer provides full coverage because today's production codes solve more complex equations using more powerful algorithms. By verifying the order-of-accuracy of the numerical algorithm implemented in the code, one can detect most any coding mistake that would prevent correct solutions from being computed. Verification of Computer Codes in Computational Science and Engineering sets forth a powerful alternative called OVMSP: Order-Verification via the Manufactured Solution Procedure. This procedure has two primary components: using the Method of Manufactured Exact Solutions to create analytic solutions to the fully-general differential equations solved by the code and using grid convergence studies to confirm the order-of-accuracy. The authors present a step-by-step procedural guide to OVMSP implementation and demonstrate its effectiveness. Properly implemented, OVMSP offers an exciting opportunity to identify virtually all coding 'bugs' that prevent correct solution of the governing partial differential equations. Verification of Computer Codes in Computational Science and Engineering shows you how this can be done. The treatment is clear, concise, and suitable both for developers of production quality simulation software and as a reference for computational science and engineering professionals.
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Computational Grids: Generations, Adaptation & Solution Strategies (Series in Computational and Physical Processes in Mechanics and Thermal Sciences)
Graham F. Carey
Manufacturer: CRC
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Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
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An Introduction to Multigrid Methods
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The Finite Element Method: Its Basis and Fundamentals, Sixth Edition
ASIN: 1560326352 |
Book Description
In this comprehensive volume a treatment of grid generation, adaptive refinement, and redistribution techniques is developed together with supporting mathematical, algorithmic, and software concepts. Efficient solution strategies that exploit grid hierarchies are also described and analyzed. Emphasis is on the fundamental ideas, but the presentation includes practical guidelines for designing and implementing grid strategies.
Customer Reviews:
Grids and Solutions.......2000-04-27
The title is a bit misleading. It is a book about solutions(finite-element method) and adaptations. You can learn how to generate and modify(adaptation) the computational grid (mainly triangular)for solutions by finite-element method. It is a bit too mathematical, but not too much for engineers to read. Many algorithms are described such as Delaunay triangulation, and also data structures for adaptation. A useful book to those who wants to learn about solution adaptation procedure.
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Multigrid Methods V: Proceedings of the Fifth European Multigrid Conference held in Stuttgart, Germany, October 1-4, 1996 (Lecture Notes in Computational Science and Engineering)
Manufacturer: Springer
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ASIN: 354063133X |
Book Description
This book is the proceedings of a top-quality meeting on multigrid methods and will become a standard reference for researchers in computational science and engineering as well as numerical analysis.
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Computational Methods For PDE In Mechanics (Series on Advances in Mathematics for Applied Sciences)
Berardino D'Acunto
Manufacturer: World Scientific Publishing Company
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ASIN: 9812560378 |
Book Description
This book provides a good introduction to modern computational methods for Partial Differential Equations in Mechanics. Finite-difference methods for parabolic, hyperbolic as well as elliptic partial differential equations are discussed.
A gradual and inductive approach to the numerical concepts has been used, such that the presentation of the theory is easily accessible to upper-level undergraduate and graduate students. Special attention has been given to the applications, with many examples and exercises provided along with solutions. For each type of equation, physical models are carefully derived and presented in full details.
Windows programs developed in C++ language have been included in the accompanying CD-ROM. These programs can be easily modified to solve different problems, and the reader is encouraged to take full advantage of the innovative features of this powerful development tool.
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Transform Methods for Solving Partial Differential Equations (Symbolic and Numeric Computation Series)
Manufacturer: CRC-Press
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Introduction to Tensor Calculus and Continuum Mechanics
ASIN: 0849373743 |
Book Description
For most scientists and engineers, the only analytic technique for solving linear partial differential equations is separation of variables. In Transform Methods for Solving Partial Differential Equations, the author uses the power of complex variables to demonstrate how Laplace and Fourier transforms can be harnessed to solve many practical, everyday problems experienced by scientists and engineers. Unlike many mathematics texts, this book provides a step-by-step analysis of problems taken from scientific and engineering literature. Detailed solutions are given in the back of the book. This essential text/reference draws from the latest literature on transform methods to provide in-depth discussions on the joint transform problem, the Cagniard-de Hoop method, and the Wiener-Hopf technique. Some 1,500 references are included as well.
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Numerical Solution of Partial Differential Equations On Parallel Computers (LECTURE NOTES IN COMPUTATIONAL SCIENCE/ ENGINEERING)
A.M Bruasat
Manufacturer: Springer
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The Sourcebook of Parallel Computing (The Morgan Kaufmann Series in Computer Architecture and Design)
ASIN: 3540290761 |
Book Description
This book surveys the major topics that are essential to high-performance simulation on parallel computers or computational clusters. These topics, including programming models, load balancing, mesh generation, efficient numerical solvers, and scientific software, are vital ingredients in the research fields of computer science, numerical analysis, and scientific computing. In addition to presenting the technological basis, this volume addresses selected applications that combine different techniques in order to meet demanding computational challenges. Through contributions from a wide range of internationally acknowledged experts, this book gives a to-the-point and self-containing overview of efficient ways to deal with large-scale simulation problems.
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Theodore Roosevelt: The Making of a Conservationist
Paul Russell Cutright
Manufacturer: University of Illinois Press
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ASIN: 0252011902 |
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Handbook of Exact Solutions for Ordinary Differential Equations
Handbook Of Linear Partial Differential Equations For Engineers And Scientists
Handbook of Integral Equations
Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition
Handbook of First-Order Partial Differential Equations (Differential and Integral Equations and Their Applications)
