Interpolation correction for collocation solutions of Fredholm integro-differential equations

In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size . Based on this expansion, ideal multilevel correction results of this collocation solution are obtained.