This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

in this work, we present a numerical method for solving nonlinear fredholmand volterra integral equations of the second kind which is based on the useof block pulse functions(bpfs) and collocation method. numerical examplesshow eciency of the method.

In this paper, He‘s variational iteration method is applied to Fredholm integral equations of the second kind. To illustrate the ability and simplicity of the method, some examples are provided. The results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.

In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method.