Solution of system of the mixed Volterra–Fredholm integral equations by an analytical method

In this paper, we present an analytical method to solve systems of the mixed Volterra–Fredholm integral equations (VFIEs) of the second kind. By using the so called $ħ$-curves, we determine the convergence parameter $ħ$, which plays a key role to control convergence of approximation solution series. Further, we show that the homotopy perturbation method (HPM), which is a well-known tool for solving systems of integral equations, is only the special case of the presented method. Some test examples are given to clarify the efficiency and high accuracy of the method. An efficient error estimation for the approximate solution is also presented for the proposed method.