چکیده (انگلیسی):

In this paper the existence, uniqueness, regularity properties, and in particular, the local representation of solutions for general Volterra functional integral equations with non- vanishing delays, are investigated. Based on the solution representation, we detailedly an- alyze the attainable (global and local) convergence order of (iterated) collocation solutions on θ-invariant meshes. It turns out that collocation at the m Gauss (-Legendre) points nei- ther leads to the optimal global convergence order m + 1, nor yields the local convergence order 2 m on the whole interval, which is in sharp contrast to the case of the classical Volterra delay integral equations. However, if the collocation is based on the m Radau II points, the local superconvergence order 2 m −1 will exhibit at all mesh points. Finally, some numerical experiments are performed to confirm our theoretical findings.