Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran.
In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy of the proposed numerical scheme is examined by comparing with other analytical and numerical results. The existence, uniqueness and convergence of the proposed method are proved. Example is presented to illustrate the efficiency and the performance of the homotopy analysis method.