Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

The paper provides an exact analytical solution to a hypersingular inregro-differential equation of arbitrary order. is defined on closed curve in the complex plane. A characteristic feature that if written using determinants. From view traditional classification equations, it should be classified as linear equations with vatiable coefficients special form. method continuation id applied. reduc...