Numerical Solution of Ordinary Differential Equations

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John Wiley & Sons, Feb 9, 2009 - Mathematics - 252 pages
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 MATLABŪ 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.

 

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Contents

Introduction
1
Eulers method
15
Problems
32
Systems of differential equations
37
Problems
46
Problems
62
Problems
89
Multistep methods
95
Stiff differential equations
127
Implicit RK methods for stiff differential equations
149
Differential algebraic equations
163
Twopoint boundary value problems
187
Volterra integral equations
211
Problems
231
Appendix B Polynomial interpolation
241
Index
250

Problems
106
Problems
123

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About the author (2009)

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.

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