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Author : Christopher T. H. Baker,Chris Phillips
Publisher : Oxford University Press, USA
Page : 392 pages
File Size : 47,5 Mb
Release : 1981
Category : Language Arts & Disciplines
ISBN : UCAL:B4980150
Author : John R. Hauser
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 55,9 Mb
Release : 2009-03-24
Category : Technology & Engineering
ISBN : 9781402099205
There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.
Author : Roland Glowinski
Publisher : Springer Science & Business Media
Page : 506 pages
File Size : 45,6 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783662126134
This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids. Finite element approximations and non-linear relaxation, and nonlinear least square methods are all covered in detail, as are many applications. This volume is a classic in a long-awaited softcover re-edition.
Author : R. Glowinski
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 51,5 Mb
Release : 2008-01-22
Category : Mathematics
ISBN : 9783540775065
When Herb Keller suggested, more than two years ago, that we update our lectures held at the Tata Institute of Fundamental Research in 1977, and then have it published in the collection Springer Series in Computational Physics, we thought, at first, that it would be an easy task. Actually, we realized very quickly that it would be more complicated than what it seemed at first glance, for several reasons: 1. The first version of Numerical Methods for Nonlinear Variational Problems was, in fact, part of a set of monographs on numerical mat- matics published, in a short span of time, by the Tata Institute of Fun- mental Research in its well-known series Lectures on Mathematics and Physics; as might be expected, the first version systematically used the material of the above monographs, this being particularly true for Lectures on the Finite Element Method by P. G. Ciarlet and Lectures on Optimization—Theory and Algorithms by J. Cea. This second version had to be more self-contained. This necessity led to some minor additions in Chapters I-IV of the original version, and to the introduction of a chapter (namely, Chapter Y of this book) on relaxation methods, since these methods play an important role in various parts of this book.
Author : E.L. Allgöwer,K. Glashoff,H.-O. Peitgen
Publisher : Springer
Page : 457 pages
File Size : 49,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387817
Author : Sören Bartels
Publisher : Springer
Page : 394 pages
File Size : 41,7 Mb
Release : 2015-01-19
Category : Mathematics
ISBN : 9783319137971
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Author : Milan Kubicek,Vladimir Hlavacek
Publisher : Courier Corporation
Page : 338 pages
File Size : 48,8 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486463001
A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.
Author : J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Publisher : Springer Nature
Page : 231 pages
File Size : 55,7 Mb
Release : 2020-02-19
Category : Mathematics
ISBN : 9783030371418
This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.
Author : George D. Byrne,Charles A. Hall
Publisher : Elsevier
Page : 430 pages
File Size : 43,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269306
Numerical Solution of Systems of Nonlinear Algebraic Equations contains invited lectures of the NSF-CBMS Regional Conference on the Numerical Solution of Nonlinear Algebraic Systems with Applications to Problems in Physics, Engineering and Economics, held on July 10-14, 1972. This book is composed of 10 chapters and begins with the concepts of nonlinear algebraic equations in continuum mechanics. The succeeding chapters deal with the numerical solution of quasilinear elliptic equations, the nonlinear systems in semi-infinite programming, and the solution of large systems of linear algebraic equations. These topics are followed by a survey of some computational techniques for the nonlinear least squares problem. The remaining chapters explore the problem of nonlinear functional minimization, the modification methods, and the computer-oriented algorithms for solving system. These chapters also examine the principles of contractor theory of solving equations. This book will prove useful to undergraduate and graduate students.
Author : Peter Deuflhard
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 48,9 Mb
Release : 2005-01-13
Category : Mathematics
ISBN : 3540210997
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.
Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 51,7 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author : You-He Zhou
Publisher : Springer Nature
Page : 478 pages
File Size : 51,8 Mb
Release : 2021-03-09
Category : Technology & Engineering
ISBN : 9789813366435
This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.
Author : Roland Glowinski
Publisher : SIAM
Page : 481 pages
File Size : 50,7 Mb
Release : 2015-11-04
Category : Mathematics
ISBN : 9781611973785
Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems?addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.
Author : James M. Ortega,Werner C. Rheinboldt
Publisher : Unknown
Page : 164 pages
File Size : 52,5 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015017336093
Author : István Faragó,János Karátson
Publisher : Nova Publishers
Page : 424 pages
File Size : 49,5 Mb
Release : 2002
Category : Mathematics
ISBN : 1590333764
Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators - Theory & Applications