Numerical Methods for Ordinary Differential Equations
Author: J. C. Butcher | Size: 3.12 MB | Format:DjVu | Quality:Unspecified | Publisher: Wiley | Year: July 28, 2003 | pages: 440 | ISBN: 0471967580, ISBN-13: 978-0471967583
In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This book is a fully revised update of the author’s classic 1987 text, Numerical Analysis of Ordinary Differential Equations, and includes more material on linear multistep methods, whilst maintaining its emphasis on Runge–Kutta methods. It contains introductory material on differential and difference equations, and a comprehensive review of numerical methods and their potential applications. The review starts from the Euler method applied to simple problems and builds on these ideas to introduce increasingly complex methods and problems. The author then explores Runge–Kutta, linear multistep and general linear methods in detail.
Provides a comprehensive introduction to numerical methods for solving ordinary differential equations.
Features introductory material on differential and difference equations.
Includes detailed coverage of Runge–Kutta, linear multistep, and general linear methods.
Contains exercises integrated into each chapter, enabling use as a course text or for self-study.
Balances informal discussion with a rigorous mathematical style.
Written by a leading authority on numerical methods.
Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving ordinary differential equations. It stands out amongst other books on the subject because of the author’s lucid writing style, and the integrated presentation of theory, examples, and exercises.
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Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.
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Finite element methods (FEM), and its associated computer software have been widely accepted as one of the most effective general tools for solving large-scale, practical engineering and science applications. For implicit finite element codes, it is a well-known fact that efficient equation and eigen-solvers play critical roles in solving large-scale, practical engineering/science problems. Sparse matrix technologies have been evolved and become mature enough that all popular, commercialized FEM codes have already inserted sparse solvers into their software. However, a few FEM books have detailed discussions about Lanczos eigen-solvers, or explain domain decomposition (DD) finite element formulation (including detailed hand-calculator numerical examples) for parallel computing purposes. The materials from this book have been evolved over the past several years through the author's research work, and graduate courses.
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This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
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This book is an introduction to modern numerical methods in engineering. It covers applications in fluid mechanics, structural mechanics, and heat transfer as the most relevant fields for engineering disciplines such as computational engineering, scientific computing, mechanical engineering as well as chemical and civil engineering. The content covers all aspects in the interdisciplinary field which are essential for an ''up-to-date'' engineer.
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The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix.
NOTE:
This is just first 7 chapters + Index.
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Dear Moderators (First of all- Thanks for your hard work here-I personally appreciate it very much)
If I have some spare time and I want to refresh some of the dead links, would not it be very handy to have a section -which the users list the dead links.
We would just go to that section and spend some time to upload a mirror link.
I remember some discussions about link alive button to be available on the threads.
May be this would be helpful mean-time
since it is simple to implement_I think_
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