Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations

The aim of this paper is to carry out an improved analysis the convergence Nyström and degenerate kernel methods their superconvergent versions for numerical solution a class linear Fredholm integro-differential equations second kind. By using interpolatory projection at Gauss points onto space (discontinuous) piecewise polynomial functions degree ?r?1, we obtain order 2r methods, while, iterated theses obtained orders are 3r+1 4r, respectively. Moreover, show that optimal 4r restored partition knots approximate solutions. theoretical results illustrated by some examples.