Generating numerical algorithms using a computer algebra system

An useful application of computer algebra systems is the generation of algorithms for numerical computations. We have shown in Gander and Gruntz (SIAM Rev., 1999) how computer algebra can be used in teaching to derive numerical methods. In this paper we extend this work, using essentially the capability of computer algebra system to construct and manipulate the interpolating polynomial and to compute a series expansion of a function. We will automatically generate formulas for integration and differentiation with error terms and also generate multistep methods for integrating differential equations.