High-order collocation methods for singular Volterra functional equations of neutral type

In the first part of this paper we present a survey of recent results on the attainable order of (super-) convergence of collocation solutions for systems of Volterra functional integro-differential equations with weakly singular kernels kα and variable delay functions θ(t)=t−τ(t). Related functional equations and theoretical and computational aspects of collocation methods for their solution are also described. The paper concludes with comments on ongoing and possible future work.