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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:

Pure and Applied Mathematics: A Wiley-Interscience Series of #81: Numerical Solution of Ordinary Differential Equations

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Pure and Applied Mathematics: A Wiley-Interscience Series of #81: Numerical Solution of Ordinary Differential Equations Cover

 

Synopses & Reviews

Publisher Comments:

A concise introduction to numerical methodsand the mathematical framework neededto understand their performance

Numerical Solution of Ordinary Differential Equations presents 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.

Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in order to help readers comprehend the applications of ordinary differential equations. In addition, the authors' collective academic experience ensures 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 test and build their knowledge of the presented methods, and a related Web site features MATLAB® programs that facilitate the exploration of numerical methods in greater depth. Detailed references outline additional literature on both analytical and numerical aspects of ordinary differential equations for further exploration of individual topics.

Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering.

Synopsis:

Kendall E. Atkinson, PhD, is Professor Emeritus in the Departments of Mathematics and Computer Science at the University of Iowa. He has authored books and journal articles in his areas of research interest, which include the numerical solution of integral equations and boundary integral equation methods. Weimin Han, PhD, is Professor in the Department of Mathematics at the University of Iowa, where he is also Director of the interdisciplinary PhD Program in Applied Mathematical and Computational Science. Dr. Han currently focuses his research on the numerical solution of partial differential equations. David E. Stewart, PhD, is Professor and Associate Chair in the Department of Mathematics at the University of Iowa, where he is also the departmental Director of Undergraduate Studies. Dr. Stewart's research interests include numerical analysis, computational models of mechanics, scientific computing, and optimization.

Synopsis:

This precise and highly readable book provides a complete and concise introduction to classical topics in the numerical solution of ordinary differential equations (ODEs). It contains many up-to-date references to both analytical and numerical ODE literature while offering new unifying views on different problem classes. A related Web site provides MATLAB programs that let the reader explore numerical methods experimentally, as well as Graphical User Interfaces (GUIs) to make experimental exploration easier. Written by well-known authors who are proven communicators and researchers, this is an ideal reference or text for students in mathematics, engineering, and the sciences.

About the Author

"An accompanying Web site offers access to more than ten MATLAB programs." (CHOICE, December 2009)

Table of Contents

Preface.

Introduction.

1. Theory of differential equations: an introduction.

1.1 General solvability theory.

1.2 Stability of the initial value problem.

1.3 Direction fields.

Problems.

2. Euler’s method.

2.1 Euler’s method.

2.2 Error analysis of Euler’s method.

2.3 Asymptotic error analysis.

2.3.1 Richardson extrapolation.

2.4 Numerical stability.

2.4.1 Rounding error accumulation.

Problems.

3. Systems of differential equations.

3.1 Higher order differential equations.

3.2 Numerical methods for systems.

Problems.

4. The backward Euler method and the trapezoidal method.

4.1 The backward Euler method.

4.2 The trapezoidal method.

Problems.

5. Taylor and Runge-Kutta methods.

5.1 Taylor methods.

5.2 Runge-Kutta methods.

5.3 Convergence, stability, and asymptotic error.

5.4 Runge-Kutta-Fehlberg methods.

5.5 Matlab codes.

5.6 Implicit Runge-Kutta methods.

Problems.

6. Multistep methods.

6.1 Adams-Bashforth methods.

6.2 Adams-Moulton methods.

6.3 Computer codes.

Problems.

7. General error analysis for multistep methods.

7.1 Truncation error.

7.2 Convergence.

7.3 A general error analysis.

Problems.

8. Stiff differential equations.

8.1 The method of lines for a parabolic equation.

8.2 Backward differentiation formulas.

8.3 Stability regions for multistep methods.

8.4 Additional sources of difficulty.

8.5 Solving the finite difference method.

8.6 Computer codes.

Problems.

9. Implicit RK methods for stiff differential equations.

9.1 Families of implicit Runge-Kutta methods.

9.2 Stability of Runge-Kutta methods.

9.3 Order reduction.

9.4 Runge-Kutta methods for stiff equations in practice.

Problems.

10. Differential algebraic equations.

10.1 Initial conditions and drift.

10.2 DAEs as stiff differential equations.

10.3 Numerical issues: higher index problems.

10.4 Backward differentiation methods for DAEs.

10.5 Runge-Kutta methods for DAEs.

10.6 Index three problems from mechanics.

10.7 Higher index DAEs.

Problems.

11. Two-point boundary value problems.

11.1 A finite difference method.

11.2 Nonlinear two-point boundary value problems.

Problems.

12. Volterra integral equations.

12.1 Solvability theory.

12.2 Numerical methods.

12.3 Numerical methods - Theory.

Problems.

Appendix A. Taylor’s theorem.

Appendix B. Polynomial interpolation.

Bibliography.

Index.

Product Details

ISBN:
9780470042946
Author:
Atkinson, Kendall E.
Publisher:
John Wiley & Sons
Author:
Han, Weimin
Author:
Atkinson, Kendall
Author:
Stewart, David
Author:
Stewart, David W.
Author:
Stewart, David E.
Subject:
Differential Equations
Subject:
Numerical solutions
Subject:
ODE
Subject:
experimental exploration
Subject:
MATLAB
Subject:
Graphical user interfaces
Subject:
Numerical methods
Subject:
Numerical analysis
Subject:
Differential equations -- Numerical solutions.
Subject:
ordinary differential equations, ODE, experimental exploration, MATLAB, Graphical User Interfaces, numerical methods, numerical analysis
Subject:
Mathematics-Differential Equations
Subject:
ordinary differential equations, ODE, experimental exploration, MATLAB, Graphical User Interfaces, numerical methods, numerical a
Subject:
nalysis
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Series Volume:
81
Publication Date:
February 2009
Binding:
HARDCOVER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Y
Pages:
252
Dimensions:
9.30x6.20x.80 in. 1.10 lbs.

Related Subjects

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Science and Mathematics » Mathematics » Differential Equations

Pure and Applied Mathematics: A Wiley-Interscience Series of #81: Numerical Solution of Ordinary Differential Equations New Hardcover
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$125.25 Backorder
Product details 252 pages John Wiley & Sons - English 9780470042946 Reviews:
"Synopsis" by , Kendall E. Atkinson, PhD, is Professor Emeritus in the Departments of Mathematics and Computer Science at the University of Iowa. He has authored books and journal articles in his areas of research interest, which include the numerical solution of integral equations and boundary integral equation methods. Weimin Han, PhD, is Professor in the Department of Mathematics at the University of Iowa, where he is also Director of the interdisciplinary PhD Program in Applied Mathematical and Computational Science. Dr. Han currently focuses his research on the numerical solution of partial differential equations. David E. Stewart, PhD, is Professor and Associate Chair in the Department of Mathematics at the University of Iowa, where he is also the departmental Director of Undergraduate Studies. Dr. Stewart's research interests include numerical analysis, computational models of mechanics, scientific computing, and optimization.
"Synopsis" by , This precise and highly readable book provides a complete and concise introduction to classical topics in the numerical solution of ordinary differential equations (ODEs). It contains many up-to-date references to both analytical and numerical ODE literature while offering new unifying views on different problem classes. A related Web site provides MATLAB programs that let the reader explore numerical methods experimentally, as well as Graphical User Interfaces (GUIs) to make experimental exploration easier. Written by well-known authors who are proven communicators and researchers, this is an ideal reference or text for students in mathematics, engineering, and the sciences.
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