A Uniformly Convergent Sequence of Spline Quadratures for Cauchy Principal Value Integrals

C. Dagnino , V. Demichelis
Department of Mathematics, Faculty of Scienze Matematiche Fisiche e Naturali, University of Torino, 10100 Torino, Italy
Received 30 January, 2009; accepted in revised form 13 October, 2011
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.

 

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