We consider the Gauss formula for an integral, integral (1)(-1) y(x) dx approximate to Sigma (N)(k=1) w(k)y(x(k)) and introduce a procedure for calculating the weights w(k) and the abscissa points x(k), k = 1, 2,.... N, such that the formula becomes best tuned to oscillatory functions of the form y(x) = f(1) (x) sin(wx) + f(2)(x) cos(wx) where f(1)(x) and f(2)(x) are smooth. The weights and the abscissas of the new formula depend on omega and, by the very construction, the formula is exact for any omega provided f(1)(x) and f(2)(x) are polynomials of class PN-1. Numerical illustrations are given for N between one and six.

A Gauss quadrature rule for oscillatory integrands

PATERNOSTER, Beatrice
2001-01-01

Abstract

We consider the Gauss formula for an integral, integral (1)(-1) y(x) dx approximate to Sigma (N)(k=1) w(k)y(x(k)) and introduce a procedure for calculating the weights w(k) and the abscissa points x(k), k = 1, 2,.... N, such that the formula becomes best tuned to oscillatory functions of the form y(x) = f(1) (x) sin(wx) + f(2)(x) cos(wx) where f(1)(x) and f(2)(x) are smooth. The weights and the abscissas of the new formula depend on omega and, by the very construction, the formula is exact for any omega provided f(1)(x) and f(2)(x) are polynomials of class PN-1. Numerical illustrations are given for N between one and six.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1000192
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 41
  • ???jsp.display-item.citation.isi??? 33
social impact