The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays

We analyze the attainable order of convergence of collocation solutions for linear and nonlinear Volterra functional integro-differential equations of neutral type containing weakly singular kernels and nonvanishing delays. The discretization of the initial-value problem is based on a reformulation as a sequence of ODEs with nonsmooth solutions. The paper concludes with a brief description of possible alternative numerical approaches for solving various classes of such functional integro-differential equations.