The Numerical Treatment Of Differential Equations

Author : Lothar Collatz
Publisher : Springer Science & Business Media
Page : 584 pages
File Size : 48,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662055007

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The Numerical Treatment of Differential Equations by Lothar Collatz Pdf

VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal.

Author : Christian Grossmann,Hans-Görg Roos,Martin Stynes
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 47,7 Mb
Release : 2007-08-11
Category : Mathematics
ISBN : 9783540715849

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Numerical Treatment of Partial Differential Equations by Christian Grossmann,Hans-Görg Roos,Martin Stynes Pdf

This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.

Author : Lothar Collatz
Publisher : Springer
Page : 568 pages
File Size : 48,7 Mb
Release : 2012-05-19
Category : Mathematics
ISBN : 3642884350

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The Numerical Treatment of Differential Equations by Lothar Collatz Pdf

This book constitutes an attempt to present in a connected fashion some of the most important numerical methods for the solution of ordinary and partial differential equations. The field to be covered is extremely wide, and it is clear that the present treatment cannot be remotely exhaustive; in particular, for partial differential equations it has only been possible to present the basic ideas, and many of the methods developed extensively by workers in applied fields - hydro dynamics, aerodynamics, etc. -, most of which have been developed for specific problems, have had to be dismissed with little more than a reference to the literature. However, the aim of the book is not so much to reproduce these special methods, their corresponding computing schemes, etc. , as to acquaint a wide circle of engineers, physicists and mathematicians with the general methods, and to show with the aid of numerous worked examples that an idea of the quantitative behaviour of the solution of a differential equation problem can be obtained by numerical means with nothing like the trouble and labour that widespread prejudice would suggest. This prejudice may be partly due to the kind of mathe matical instruction given in technical colleges and universities, in which, although the theory of differential equations is dealt with in detail, numerical methods are gone into only briefly.

Author : W. Hackbusch
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 44,6 Mb
Release : 1992
Category : Language Arts & Disciplines
ISBN : 354054822X

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Elliptic Differential Equations by W. Hackbusch Pdf

Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR

Author : Lothar Collatz,P. G. Williams
Publisher : Springer
Page : 0 pages
File Size : 55,6 Mb
Release : 1960
Category : Mathematics
ISBN : 3662249340

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The Numerical Treatment of Differential Equations by Lothar Collatz,P. G. Williams Pdf

This book constitutes an attempt to present in a connected fashion some of the most important numerical methods for the solution of ordinary and partial differential equations. The field to be covered is extremely wide, and it is clear that the present treatment cannot be remotely exhaustive; in particular, for partial differential equations it has only been possible to present the basic ideas, and many of the methods developed extensively by workers in applied fields - hydro dynamies, aerodynamics, etc. -, most of which have been developed for specific problems, have had to be dismissed with little more than a reference to the literature. However, the aim of the book is not so much to reproduce these special methods, their corresponding computing schemes, etc. , as to acquaint a wide circ1e of engineers, physicists and mathematicians with the general methods, and to show with the aid of numerous worked examples that an idea of the quantitative behaviour of the solution of a differential equation problem can be obtained by numerical means with nothing like the trouble and labour that widespread prejudice would suggest. This prejudice may be partly due to the kind of mathe matical instruction given in technical colleges and universities, in which, although the theory of differential equations is dealt with in detail, numerical methods are gone into only briefly.

Author : Peter E. Kloeden,Eckhard Platen
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 53,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662126165

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Numerical Solution of Stochastic Differential Equations by Peter E. Kloeden,Eckhard Platen Pdf

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Author : R. Bulirsch,R. D. Grigorieff,J. Schroder
Publisher : Unknown
Page : 236 pages
File Size : 54,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662172577

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Numerical Treatment of Differential Equations by R. Bulirsch,R. D. Grigorieff,J. Schroder Pdf

Author : Heinz-Otto Kreiss,Hedwig Ulmer Busenhart
Publisher : Birkhäuser
Page : 87 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882293

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Time-dependent Partial Differential Equations and Their Numerical Solution by Heinz-Otto Kreiss,Hedwig Ulmer Busenhart Pdf

This book studies time-dependent partial differential equations and their numerical solution, developing the analytic and the numerical theory in parallel, and placing special emphasis on the discretization of boundary conditions. The theoretical results are then applied to Newtonian and non-Newtonian flows, two-phase flows and geophysical problems. This book will be a useful introduction to the field for applied mathematicians and graduate students.

Author : Ernst Hairer,Christian Lubich,Michel Roche
Publisher : Springer
Page : 146 pages
File Size : 40,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468325

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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods by Ernst Hairer,Christian Lubich,Michel Roche Pdf

The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.

Author : Wolfgang Hackbusch
Publisher : Springer
Page : 455 pages
File Size : 50,8 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783662549612

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Elliptic Differential Equations by Wolfgang Hackbusch Pdf

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Author : Nik Pachis
Publisher : Unknown
Page : 280 pages
File Size : 55,6 Mb
Release : 2016-04-01
Category : Electronic
ISBN : 1681174480

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Numerical Solution of Ordinary Differential Equations by Nik Pachis Pdf

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term is sometimes taken to mean the computation of integrals. An ordinary differential equation or ODE is a differential equation containing one or more functions of one independent variable and its derivatives. The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. Ordinary differential equations are ubiquitous in science and engineering: in geometry and mechanics from the first examples onwards (Newton, Leibniz, Euler, Lagrange), in chemical reaction kinetics, molecular dynamics, electronic circuits, population dynamics, and many more application areas. They also arise, after semi discretization in space, in the numerical treatment of time-dependent partial differential equations, which are even more impressively omnipresent in our technologically developed and financially controlled world. The book Numerical Solution of Ordinary Differential Equations offers a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems.

Author : R. Bulirsch,R.D. Grigorieff,J. Schröder
Publisher : Springer
Page : 232 pages
File Size : 49,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540359708

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Numerical Treatment of Differential Equations by R. Bulirsch,R.D. Grigorieff,J. Schröder Pdf

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 40,6 Mb
Release : 1986
Category : Electronic
ISBN : OCLC:456645648

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Numerical Treatment of Differential Equations by Anonim Pdf

Author : Claes Johnson
Publisher : Courier Corporation
Page : 290 pages
File Size : 45,9 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131597

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Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson Pdf

An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 486 pages
File Size : 42,7 Mb
Release : 2008-04-15
Category : Mathematics
ISBN : 0470753757

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Numerical Methods for Ordinary Differential Equations by J. C. Butcher Pdf

In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book include Introductory work on differential and difference equations. A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically. A detailed analysis of Runge-Kutta methods and of linear multistep methods. A complete study of general linear methods from both theoretical and practical points of view. The latest results on practical general linear methods and their implementation. A balance between informal discussion and rigorous mathematical style. Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise. Written in a lucid style by one of the worlds leading authorities on numerical methods for ordinary differential equations and drawing upon his vast experience, this new edition provides an accessible and self-contained introduction, ideal for researchers and students following courses on numerical methods, engineering and other sciences.