Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations

In this paper, polynomial-based superconvergent degenerate kernel and {Nyström} methods for solving {Fredholm} integral equations of the second kind with  the smooth kernel are studied. By using an interpolatory projection based on Legendre polynomials of degree \leq n, we analyze the convergence of these methods and we establish superconvergence results for their iterated versions. Two numerical examples are given to illustrate the theoretical estimates.

Keywords:

Fredholm integral equations , Degenerate kernel and Nystr¨om methods , Legendre polynomials , Interpolatory projection , Superconvergence rates