Numerical Methods For Ordinary Differential Systems

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Numerical Methods for Ordinary Differential Equations

David F. Griffiths,Desmond J. Higham
Numerical Methods for Ordinary Differential Equations Book PDF

Author : David F. Griffiths,Desmond J. Higham
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 52,9 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

Numerical Methods for Ordinary Differential Equations

J. C. Butcher
Numerical Methods for Ordinary Differential Equations Book PDF

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 442 pages
File Size : 52,7 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.

Numerical Solution of Ordinary Differential Equations

Kendall Atkinson,Weimin Han,David E. Stewart
Numerical Solution of Ordinary Differential Equations Book PDF

Author : Kendall Atkinson,Weimin Han,David E. Stewart
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 55,5 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.

Numerical Methods for Ordinary Differential Equations

J. C. Butcher
Numerical Methods for Ordinary Differential Equations Book PDF

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 546 pages
File Size : 54,9 Mb
Release : 2016-08-29
Category : Mathematics
ISBN : 9781119121503

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

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.

Numerical Methods for Ordinary Differential Systems

J. D. Lambert
Numerical Methods for Ordinary Differential Systems Book PDF

Author : J. D. Lambert
Publisher : Wiley-Blackwell
Page : 293 pages
File Size : 51,5 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.

Finite Difference Methods for Ordinary and Partial Differential Equations

Randall J. LeVeque
Finite Difference Methods for Ordinary and Partial Differential Equations Book PDF

Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 51,8 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.

Numerical Methods for Evolutionary Differential Equations

Uri M. Ascher
Numerical Methods for Evolutionary Differential Equations Book PDF

Author : Uri M. Ascher
Publisher : SIAM
Page : 403 pages
File Size : 48,8 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.

A First Course in the Numerical Analysis of Differential Equations

A. Iserles
A First Course in the Numerical Analysis of Differential Equations Book PDF

Author : A. Iserles
Publisher : Cambridge University Press
Page : 481 pages
File Size : 45,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780521734905

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A First Course in the Numerical Analysis of Differential Equations by A. Iserles Pdf

lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

The Numerical Analysis of Ordinary Differential Equations

J. C. Butcher
The Numerical Analysis of Ordinary Differential Equations Book PDF

Author : J. C. Butcher
Publisher : Unknown
Page : 538 pages
File Size : 41,8 Mb
Release : 1987-02-24
Category : Mathematics
ISBN : UOM:39015017314330

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The Numerical Analysis of Ordinary Differential Equations by J. C. Butcher Pdf

Mathematical and computational introduction. The Euler method and its generalizations. Analysis of Runge-Kutta methods. General linear methods.

Analytic Methods for Partial Differential Equations

G. Evans,J. Blackledge,P. Yardley
Analytic Methods for Partial Differential Equations Book PDF

Author : G. Evans,J. Blackledge,P. Yardley
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447103790

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Analytic Methods for Partial Differential Equations by G. Evans,J. Blackledge,P. Yardley Pdf

This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.

Numerical Methods for Differential Equations

J.R. Dormand
Numerical Methods for Differential Equations Book PDF

Author : J.R. Dormand
Publisher : CRC Press
Page : 385 pages
File Size : 46,5 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.

Solving Ordinary Differential Equations I

Ernst Hairer,Syvert P. Nørsett,Gerhard Wanner
Solving Ordinary Differential Equations I Book PDF

Author : Ernst Hairer,Syvert P. Nørsett,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 541 pages
File Size : 55,7 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.

Numerical Solution of Ordinary Differential Equations

L.F. Shampine
Numerical Solution of Ordinary Differential Equations Book PDF

Author : L.F. Shampine
Publisher : Routledge
Page : 632 pages
File Size : 43,8 Mb
Release : 2018-10-24
Category : Mathematics
ISBN : 9781351427555

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Numerical Solution of Ordinary Differential Equations by L.F. Shampine Pdf

This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.

The Numerical Solution of Ordinary and Partial Differential Equations

Granville Sewell
The Numerical Solution of Ordinary and Partial Differential Equations Book PDF

Author : Granville Sewell
Publisher : World Scientific
Page : 348 pages
File Size : 49,6 Mb
Release : 2014-12-16
Category : Mathematics
ISBN : 9789814635110

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The Numerical Solution of Ordinary and Partial Differential Equations by Granville Sewell Pdf

This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A. The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions. Contents:Direct Solution of Linear SystemsInitial Value Ordinary Differential EquationsThe Initial Value Diffusion ProblemThe Initial Value Transport and Wave ProblemsBoundary Value ProblemsThe Finite Element MethodsAppendix A — Solving PDEs with PDE2DAppendix B — The Fourier Stability MethodAppendix C — MATLAB ProgramsAppendix D — Answers to Selected Exercises Readership: Undergraduate, graduate students and researchers. Key Features:The discussion of stability, absolute stability and stiffness in Chapter 1 is clearer than in other textsStudents will actually learn to write programs solving a range of simple PDEs using the finite element method in chapter 5In Appendix A, students will be able to solve quite difficult PDEs, using the author's software package, PDE2D. (a free version is available which solves small to moderate sized problems)Keywords:Differential Equations;Partial Differential Equations;Finite Element Method;Finite Difference Method;Computational Science;Numerical AnalysisReviews: "This book is very well written and it is relatively easy to read. The presentation is clear and straightforward but quite rigorous. This book is suitable for a course on the numerical solution of ODEs and PDEs problems, designed for senior level undergraduate or beginning level graduate students. The numerical techniques for solving problems presented in the book may also be useful for experienced researchers and practitioners both from universities or industry." Andrzej Icha Pomeranian Academy in Słupsk Poland

Numerical Analysis of Ordinary Differential Equations and Its Applications

Taketomo Mitsui,Yoshitane Shinohara
Numerical Analysis of Ordinary Differential Equations and Its Applications Book PDF

Author : Taketomo Mitsui,Yoshitane Shinohara
Publisher : World Scientific
Page : 244 pages
File Size : 55,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9810222297

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Numerical Analysis of Ordinary Differential Equations and Its Applications by Taketomo Mitsui,Yoshitane Shinohara Pdf

The book collects original articles on numerical analysis of ordinary differential equations and its applications. Some of the topics covered in this volume are: discrete variable methods, Runge-Kutta methods, linear multistep methods, stability analysis, parallel implementation, self-validating numerical methods, analysis of nonlinear oscillation by numerical means, differential-algebraic and delay-differential equations, and stochastic initial value problems.