Generating Numerical Algorithms Using Computer Algebra
Walter Gander, Institute for Computational Science, ETH Zurich
Abstract: We show how numerical algorithms can be derived in a simple way using computer algebra. Examples are numerical differentiation, quadrature and multi-step methods for ODE. It is also shown how the discretization error of a method can be computed automatically. This approach not only makes formularies obsolete (in fact some errors were found in Abramowitz/Stegun) but is also useful in teaching since principles and fundamentals are emphasized and we can leave the sometimes tedious derivation of the specific algorithm to the machine.