Fredholm integral equation

SOR Homotopy perturbation method to solve integro-differential equations

We present in this paper, SOR Homotopy perturbation method, a new decomposition method by introducing a parameter $\omega$ to extend a classical homotopy perturbation method for solving integro-differential equations of various kinds.  Using SOR homotopy perturbation method and its iterative scheme we can give the exact solution or a closed approximate to the solution of the problem.  The convergence of the proposed method has been elaborated and some illustrative examples are presented with applications to Fredholm and Volterra integral equations.

Legendre–Kantorovich method for Fredholm integral equations of the second kind

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

Modeling the Electromagnetic Wave Scattering by Small Impedance Particle

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.