Generating numerical algorithms using a computer algebra system |
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Authors: | Walter Gander |
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Affiliation: | (1) Institute of Computational Science, ETH Zurich, CH-8092 Zurich, Switzerland |
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Abstract: | 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. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65D25, 65D30, 65D32, 65L06 |
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Keywords: | computer algebra numerical integration numerical differentiation multistep methods |
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