Numerical Solution of Ordinary Differential EquationsA 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:
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 |
250 | |
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Numerical Solution of Ordinary Differential Equations Kendall Atkinson,Weimin Han,David E. Stewart Limited preview - 2011 |