A modified Nyström–Clenshaw–Curtis quadrature for integral equations with piecewise smooth kernels

The Nyström–Clenshaw–Curtis (NCC) quadrature is a highly accurate quadrature which is suitable for integral equations with semi-smooth kernels. In this paper, we first introduce the NCC quadrature and point out that the NCC quadrature is not suitable for certain integral equation with well-behaved kernel functions such as e − | t − s | . We then modify the NCC quadrature to obtain a new quadrature which is suitable for integral equations with piecewise smooth kernel functions. Applications of the modified NCC quadrature to Wiener–Hopf equations and a nonlinear integral equation are presented.