Collocation methods for nonlinear convolution Volterra integral equations with multiple proportional delays

In this paper, we apply the collocation methods to a class of nonlinear convolution Volterra integral equations with multiple proportional delays (NCVIEMPDs). We shall present the existence, uniqueness and regularity properties of analytic solution for this type equation, and then analyze the convergence and superconvergence properties of the collocation solution. The numerical results verify our theoretical analysis.