Nyström-Clenshaw-Curtis quadrature for the solution of Volterra integral equations with proportional delays

The Nystrom-Clenshaw-Curtis (NCC) quadrature, which was proposed in [S. Y. Kang, I. Koltracht, and G. Rawitscher, Math. Comp. 72, 729–756 (2003)], is a highly accurate numerical method for solving integral equations with semi-smooth kernel. In this paper, we introduce the basic idea of the NCC quadrature and derive an NCC quadrature for Volterra integral equations with proportional delays. Numerical results are presented to illustrated the high accuracy of the method.