Generating Numerical Algorithms Using Computer Algebra

Walter Gander, Institute for Computational Science, ETH Zurich

Wednesday August 3rd, IRMACS.

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.