Spline Quasi-Interpolants with Boundary Interpolation Properties for Cauchy Principal Value Integrals

摘要

We propose new quadrature rules 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 computationalscheme for the quadrature weights and some numerical results are given.