Generating numerical ODE formulas via a symbolic calculus of divided differences

Divided differences of vector functions can be applied to generate numerical update formulas for ODEs, as proposed by W. Kahan. A computer algebra system renders the symbolic manipulations practical to perform. The technique is presented here using the Maple system. Some examples illustrate the pote...

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Bibliographic Details
Published in:SIGSAM bulletin 1999-06, Vol.33 (2), p.29-42
Main Author: Geddes, K. O.
Format: Article
Language:English
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Summary:Divided differences of vector functions can be applied to generate numerical update formulas for ODEs, as proposed by W. Kahan. A computer algebra system renders the symbolic manipulations practical to perform. The technique is presented here using the Maple system. Some examples illustrate the potential applications of this hybrid symbolic-numeric approach to solving initial-value problems.
ISSN:0163-5824
DOI:10.1145/334714.334717