Scientific Computing with Ordinary Differential Equations

This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical basis. The book strictly presents numerical analysis as part of the more general field of scientific computing. Important algorithmic concepts are explained down to questions of software implementation. For initial value problems, a dynamical systems approach is used to develop Runge-Kutta, extrapolation, and multistep methods. For boundary value problems, including optimal control problems, both multiple shooting and collocation methods are worked out in detail. Graduate students and researchers in mathematics, computer science, and engineering will find this book useful. Chapter summaries, detailed illustrations, and exercises are contained throughout the book, with many interesting applications taken from a rich variety of areas.