Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations

Abstract

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