A numerical method for solving nonlinear integral equations in the Urysohn form

Integral equations occur naturally in many field of mechanics andmathematical physics. In this paper, an iterative scheme based on thehomotopy analysis method (HAM) has been used for solving one of themost important cases in nonlinear integral equations which is calledurysohn form. For this scope, we applied some examples with knownexact solutions and the numerical solutions obtained confirm that themethod is very effective and simple. Also, show the advantage of thismethod, the results obtained by (HAM) are compared with Newton-Kantorovich-quadrature method. Convergence is also observed.