Fredholm integral equation

In the present paper, we consider polynomially based Kantorovich method for the numerical solution of Fredholm integral equation of the second kind with a smooth kernel.  The used projection is  either the orthogonal projection or an interpolatory projection using Legendre polynomial bases.  The order of convergence of the proposed method and those of superconvergence of the iterated versions are established.  We show that these orders of convergence are valid in the corresponding discrete methods obtained by replacing the integration by a quadrature rule.  Numerical examples are given to i

The problem of electromagnetic waves scattering on the small particle is reduced to solving the Fredholm integral equation of the second kind. Integral representation of solutions to the diffraction problem implies in determination of some auxiliary function which contains in integrand of this equation. The respective linear algebraic system for the components of this auxiliary function is derived and solved by the successive approximation method. The region of convergence of the proposed method is substantiated numerically.