Greenspan D. Numerical Solution of Ordinary Differential Equations...2006

Textbook in PDF format

This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic systems. The examples are carefully explained and compiled into an algorithm, each of which is presented independent of a specific programming language. Each chapter is rounded off with exercises.
Euler's method
Runge-Kutta methods
The method of Taylor expansions
Large second-order systems with application to nano systems
Completely conservative, covariant numerical methodology
Instability
Numerical solution of tridiagonal linear algebraic systems and related nonlinear systems
Approximate solution of boundary value problems
Special relativistic motion
Special topics