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

Authors:	C. Dagnino A. Palamara Orsi

Affiliation:	(1) Dipartimento di Energetica, Facoltà di Ingegneria, Università degli Studie de L'Aquila, I-67040 Monteluco, Roio Poggio, Italy;(2) Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy

Abstract:	Summary In this paper we consider the approximate evaluation of $intlimits_a^b {K(x)f(x)dx}$ , whereK(x) is a fixed Lebesgue integrable function, by product formulas of the form $sumlimits_{i = 0}^n {w_i f(x_i )}$ 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.Work sponsored by the Ministero della Pubblica Istruzione of Italy

Keywords:	AMS (MOS): 65D30 CR: G1.4
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