Computer generation of numerical methods for ordinary differential equations

We describe some issues related to the derivation of numerical methods for ordinary differential equations. We discuss how to establish algebraic constraints on the free parameters of the methods which control the quality of the numerical solution. Furthermore, we describe a Mathematica package which essentially automates the derivation process for Runge-Kutta methods. The package incorporates many new facilities to aid in analysis and construction and we will give examples to plain the design and motivation for the functionality. We also discuss some techniques that are useful for obtaining solutions to the algebraic constraints.