Computational Methods In Ordinary Differential Equations

Author : David F. Griffiths,Desmond J. Higham
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 55,5 Mb
Release : 2010-11-11
Category : Mathematics
ISBN : 9780857291486

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Numerical Methods for Ordinary Differential Equations by David F. Griffiths,Desmond J. Higham Pdf

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

Author : J. D. Lambert
Publisher : Unknown
Page : 278 pages
File Size : 42,8 Mb
Release : 1983
Category : Electronic
ISBN : OCLC:1024537503

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Computational Methods in Ordinary Differential Equations by J. D. Lambert Pdf

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 442 pages
File Size : 47,8 Mb
Release : 2004-08-20
Category : Mathematics
ISBN : 9780470868263

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

This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. "This book is...an indispensible reference for any researcher."-American Mathematical Society on the First Edition. Features: * New exercises included in each chapter. * Author is widely regarded as the world expert on Runge-Kutta methods * Didactic aspects of the book have been enhanced by interspersing the text with exercises. * Updated Bibliography.

Author : J.R. Dormand
Publisher : CRC Press
Page : 385 pages
File Size : 44,5 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351083553

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Numerical Methods for Differential Equations by J.R. Dormand Pdf

With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.

Author : Jack D. Lambert
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 1974
Category : Electronic
ISBN : OCLC:615111419

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Computational Methods in Ordinary Differential Equations by Jack D. Lambert Pdf

Author : Kenneth Eriksson
Publisher : Cambridge University Press
Page : 558 pages
File Size : 51,9 Mb
Release : 1996-09-05
Category : Mathematics
ISBN : 0521567386

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Computational Differential Equations by Kenneth Eriksson Pdf

This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.

Author : John Denholm Lambert
Publisher : Unknown
Page : 306 pages
File Size : 55,7 Mb
Release : 1973-02-16
Category : Mathematics
ISBN : UOM:39015049310520

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Computational Methods in Ordinary Differential Equations by John Denholm Lambert Pdf

Author : Kendall Atkinson,Weimin Han,David E. Stewart
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 53,9 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118164525

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Numerical Solution of Ordinary Differential Equations by Kendall Atkinson,Weimin Han,David E. Stewart Pdf

A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

Author : Uri M. Ascher,Linda R. Petzold
Publisher : SIAM
Page : 305 pages
File Size : 53,8 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 161197139X

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Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations by Uri M. Ascher,Linda R. Petzold Pdf

Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.

Author : Peter Deuflhard,Folkmar Bornemann
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780387215822

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Scientific Computing with Ordinary Differential Equations by Peter Deuflhard,Folkmar Bornemann Pdf

Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area

Author : Uri M. Ascher
Publisher : SIAM
Page : 403 pages
File Size : 40,6 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780898716528

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Numerical Methods for Evolutionary Differential Equations by Uri M. Ascher Pdf

Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.

Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 48,5 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717833

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Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque Pdf

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.

Author : Ernst Hairer,Syvert P. Nørsett,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 541 pages
File Size : 55,8 Mb
Release : 2008-04-03
Category : Mathematics
ISBN : 9783540788621

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Solving Ordinary Differential Equations I by Ernst Hairer,Syvert P. Nørsett,Gerhard Wanner Pdf

This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.

Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 54,8 Mb
Release : 2016-04-28
Category : Technology & Engineering
ISBN : 9781119111368

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Numerical Methods for Partial Differential Equations by Vitoriano Ruas Pdf

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

Author : J. D. Lambert
Publisher : Wiley-Blackwell
Page : 293 pages
File Size : 43,9 Mb
Release : 1991
Category : Mathematics
ISBN : 0471929905

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Numerical Methods for Ordinary Differential Systems by J. D. Lambert Pdf

Numerical Methods for Ordinary Differential Systems The Initial Value Problem J. D. Lambert Professor of Numerical Analysis University of Dundee Scotland In 1973 the author published a book entitled Computational Methods in Ordinary Differential Equations. Since then, there have been many new developments in this subject and the emphasis has changed substantially. This book reflects these changes; it is intended not as a revision of the earlier work but as a complete replacement for it. Although some basic material appears in both books, the treatment given here is generally different and there is very little overlap. In 1973 there were many methods competing for attention but more recently there has been increasing emphasis on just a few classes of methods for which sophisticated implementations now exist. This book places much more emphasis on such implementations—and on the important topic of stiffness—than did its predecessor. Also included are accounts of the structure of variable-step, variable-order methods, the Butcher and the Albrecht theories for Runge—Kutta methods, order stars and nonlinear stability theory. The author has taken a middle road between analytical rigour and a purely computational approach, key results being stated as theorems but proofs being provided only where they aid the reader’s understanding of the result. Numerous exercises, from the straightforward to the demanding, are included in the text. This book will appeal to advanced students and teachers of numerical analysis and to users of numerical methods who wish to understand how algorithms for ordinary differential systems work and, on occasion, fail to work.