On some numerical iterative methods for Fredholm integral equations with deviating arguments

Sanda Micula

Abstract


In this paper we develop iterative methods for nonlinear Fredholm
integral equations of the second kind with deviating arguments,
by applying Mann's iterative algorithm. This proves the existence and
the uniqueness of the solution and gives a better error estimate than the
classical Banach Fixed Point Theorem. The iterates are then approximated
using a suitable quadrature formula. The paper concludes with
a numerical example.

Keywords


Fredholm integral equations, deviating arguments, numerical approximations, Altman's algorithm, Mann's iterative algorithm.

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