# Numerical Solution of Ordinary Differential Equations

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