The numerical analysis of ordinary differential equations Book

MATHEMATICAL AND COMPUTATIONAL INTRODUCTION
Mathematical Preliminaries
Ordinary Differential Equations
Difference Equations
Numerical Approximation
Graphs and Combinatorics
THE EULER METHOD AND ITS GENERALIZATIONS
The Euler Method
Generalizations of the Euler Method
Runge-Kutta Methods
Linear Multistep Methods
Taylor Series Methods
ANALYSIS OF RUNGE-KUTTA METHODS
The Order Conditions
Low Order Explicit Methods
The Attainable Order of Explicit Methods
High Order Explicit Methods
Implicit Runge-Kutta Methods
Stability Properties of Runge-Kutta Methods
Error Propagation in Runge-Kutta Methods
Runge-Kutta Methods with Error Estimates
Algebraic Properties of Runge-Kutta Methods
GENERAL LINEAR METHODS
Introduction to General Linear Methods
Examples of General Linear Methods
Stability, Consistency and Convergence
Order of Accuracy
Stability Properties of General Linear Methods
Practical Prospects for General Linear Methods
Bibliography