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Numerical Methods for Ordinary Differential Equations, by J. C. Butcher
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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.
- Sales Rank: #2091722 in Books
- Published on: 2008-06-09
- Original language: English
- Number of items: 1
- Dimensions: 9.06" h x 1.21" w x 6.28" l, 1.80 pounds
- Binding: Hardcover
- 482 pages
Review
“I enjoyed reading this book.� It is well written and quite approachable.” (Mathematical Reviews, 2004c)
"…covers now all the material that is modern standard in this field… belongs into any mathematical library..." (Zentralblatt Math, Vol.1040, No.09, 2004)
�
From the Back Cover
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.
Most helpful customer reviews
5 of 5 people found the following review helpful.
Useful, Practical, Fascinating Book by A Well-Known Authority and Teacher
By Mersault
This is the Second Edition of a classic work on solving differential equations numerically. The well-known author and teacher has published pathfinding papers on this topic from the early 1960's to the present. The "Butcher Tableau" is the standard short-hand display for Runge-Kutta methods.
The book sets the table by describing a set of standard problems for numerical solution. Then, as new methods are described their efficacy on the standard problems is graphed and tabulated.
Explicit and implicit Runge-Kutta Methods, Linear Multistep Methods, Taylor Series Methods and General Linear Methods are thoroughly described from the viewpoint of accuracy and stability. Symplectic Runge-Kutta methods, 'Almost' Runge-Kutta methods and Inverse Runge-Kutta Methods are among the additional covered topics of current interest.
Practical issues for the implementer of algorithms based on these methods, such as error estimation and step-size control, are well-covered. References to the topic's literature are also outstanding.
To use the book, a background in calculus and numerical analysis is essential.
Current topics in this field are well-represented. The author has taught many of the present class of researchers, and the clarity of a great teacher is apparent.
Web resources and problems at the end of each section enhance the book's value for a semester-long course.
5 of 5 people found the following review helpful.
The Definitive Reference for ODEs
By Antony N. Beris
An in-depth analysis from one of the best experts in the field of the latest developments in the numerical solution of ODEs with special emphasis on the Runge-Kutta methods, although Linear Multistep Methods and General Linear Methods are also thoroughly described. A must read for any researcher with interest on the numerical solution of initial value problems.
1 of 1 people found the following review helpful.
Butcher rocks
By Robert
This book is outstanding. Anyone trying to get into the how's and why's of numerical ODE methods should definitely start here. Great review of Runge-Kutta methods, and I really like the introduction to linear multistep methods. Great stuff.
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