A note on collocation methods for Volterra integral equations of the first kind

It has been shown that if a Volterra integral equation of the first kind with continuous kernel is solved numerically in a given intervalI by collocation in the space of piecewise polynomials of degreem≧0 and possessing finite discontinuities at their knotsZ _N then a careful choice of the collocation points yields convergence of orderp=m+2 on a certain finite subset ofI (while the global convergence order ism+1; this subset does not contain the knotsZ _N . In this note it will be shown that superconvergence onZ _N can be attained only if some of the collocation points coalesce (Hermite-type collocation).