The numerical analysis of ordinary differential equations

the long version

A step-by-step treatment of differential equations and their solution via numerical methods. Beginning by examining differential calculus on a vector space, graphs, and combinatorics then looks at numerical methods for solving initial value problems through discussions of particular classes of methods as generalizations of Euler. This information serves as background to the detailed study of Runge-Kutta that follows and, using this as a theoretical framework, discusses general linear methods, providing a means of studying a wide range of interesting approaches in a unified manner.