In this paper we consider the approximate evaluation of baK(x)f(x)dx , whereK(x) is a fixed Lebesgue integrable function, by product formulas of the form ni=0wif(xi) based on cubic spline interpolation of the functionf. Generally, whenever it is possible, product quadratures incorporate the bad behaviour of the integrand in the kernelK. Here, however, we allowf to have a finite number of jump discontinuities in [a, b]. Convergence results are established and some numerical applications are given for a logarithmic singularity structure in the kernel.

Product integration of piecewise continuous integrands based on cubic splineinterpolation at equally spaced nodes

DAGNINO, Catterina;
1988-01-01

Abstract

In this paper we consider the approximate evaluation of baK(x)f(x)dx , whereK(x) is a fixed Lebesgue integrable function, by product formulas of the form ni=0wif(xi) based on cubic spline interpolation of the functionf. Generally, whenever it is possible, product quadratures incorporate the bad behaviour of the integrand in the kernelK. Here, however, we allowf to have a finite number of jump discontinuities in [a, b]. Convergence results are established and some numerical applications are given for a logarithmic singularity structure in the kernel.
1988
52
459
466
C Dagnino; A Palamara Orsi
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/2318/120393
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 8
social impact