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CECM Home > Events > CECM Annual Summer Meeting 2005 > Program > Abstract: Walter Gander

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Generating Numerical Algorithms Using Computer Algebra

Walter Gander · Institute for Computational Science, ETH Zurich

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.