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Oscillatory integrals by Hermite interpolatory rules

✍ Scribed by Alaylioglu, Ayse

Publisher: Wiley (John Wiley & Sons)
Year: 1986
Tongue: English
Weight: 381 KB
Volume: 2
Category: Article
ISSN: 0748-8025
DOI: 10.1002/cnm.1630020503

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✦ Synopsis

This paper is concerned with the numerical construction of Hermite interpolatory product integration rules at arbitrarily prescribed nodes. The heart of the computational scheme is the efficient construction of Hermite functions of any order for any set of points. For the purpose of illustration, quadrature formulae based on the use of Basu. Clenshaw, Filippi. Filon and Polya nodes are generated for oscillatory integrals. Of the nodes considered, Basu nodes yield the most accurate results in the interesting case of rapid oscillations, while Filippi nodes give rise to efficient common-point quadrature rules when the integrand has slight oscillations. The results also demonstrate that Hermite rules compare well with the Lagrange quadrature for the same number of function evaluations.

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