Quadrature rules using first derivatives for oscillatory integrands

We consider the integral of a function y(x), I(y(x))= ∫ −1 1 y(x) dx and its approximation by a quadrature rule of the form Q N(y(x))= ∑ k=1 N w ky(x k)+ ∑ k=1 N α ky′(x k), i.e., by a rule which uses the values of both y and its derivative at nodes of the quadrature rule. We examine the cases when...

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Veröffentlicht in:	Journal of computational and applied mathematics 2002-03, Vol.140 (1), p.479-497
Hauptverfasser:	Kim, Kyung Joong, Cools, Ronald, Ixaru, L.Gr
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Integral equations, integral transforms Integration formula Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Oscillatory integrand Quadrature rule Sciences and techniques of general use
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