We propose a new quadrature rule for Cauchy principal value integrals based on quadratic spline quasi-interpolants which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights is given. Some numerical results and comparisons with other spline methods are presented.
A uniformly convergent sequence of spline quadratures for Cauchy principal value integrals
DAGNINO, Catterina;DEMICHELIS, Vittoria
2011-01-01
Abstract
We propose a new quadrature rule for Cauchy principal value integrals based on quadratic spline quasi-interpolants which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights is given. Some numerical results and comparisons with other spline methods are presented.File in questo prodotto:
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