Spline approximation for Cauchy principal value integrals

摘要

In this paper we prove the uniform convergence of some quadrature formulas based on spline approximation for Cauchy principal value integrals of the type fbaw(x)f(k)(x)/x - y dx (k = 0, 1,…) and we present some numerical applications. In particular we apply our rules to the well-known Prandtl's integral equation.