Document Type : Research Paper


1 University Mohammed I, Team MSC, FPN, LAMAO Laboratory, Nador, 62000, Morocco.

2 University Mohammed I, Team ANAA, EST, LANO Laboratory, Oujda, 60000, Morocco.


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.


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