Includes bibliographical references (p. -266) and index.
ODEs: an introduction
The Taylor series method
Linear multistep methods I
Linear multistep methods II
Linear multistep methods III
Linear multistep methods IV
Linear multistep methods V
Runge-Kutta method I: order conditions
Runge-Kutta methods II: absolute stability
Adaptive step size selection
Geometric integration part I: invariants
Geometric integration part II: Hamiltonian dynamics
Stochastic differential equations
[Appendices]. Glossary and notation
Jacobians and variational equations
Constant-coefficient difference equations.
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical method without losing sight of the practical nature of the subject.