Textbook in PDF format

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject
The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics.
In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems.
This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.
Differential and Difference Equations
Differential Equation Problems
Differential Equation
Further Evolutionary Problems
Difference Equation Problems
Difference Equation Theory
Location of Polynomial Zeros
Numerical Differential Equation Methods
The Euler Method
Analysis of the Euler Method
Generalizations of the Euler Method
Runge–Kutta Methods
Linear
Taylor Series Methods
MultivalueMulitistage Methods
Introduction to Implementation
Runge–KuttaMethods
Preliminaries
Order Conditions
Low Order ExplicitMethods
Runge–Kutta Methods with Error Estimates
Implicit Runge–Kutta Methods
Stability of Implicit Runge–Kutta Methods
Implementable Implicit Runge–Kutta Methods
Implementation Issues
Algebraic Properties of Runge–Kutta Methods
Symplectic Runge–Kutta Methods
Linear Multistep Methods
Preliminaries
The Order of Linear MultistepMethods
Errors and Error Growth
Stability Characteristics
Order and Stability Barriers
One-leg Methods and G-stability
Implementation Issues
General Linear Methods
RepresentingMethods in General Linear Form
Consistency, Stability and Convergence
The Stability of General Linear Methods 4
The Order of General Linear Methods
Methods with Runge–Kutta stability
Methods with Inherent Runge–Kutta Stability
G-symplectic methods