A modified homotopy perturbation method for solving the nonlinear mixed Volterra–Fredholm integral equation

The purpose of this paper is to obtain the approximation solution of the strongly nonlinear mixed Volterra–Fredholm integral equation (VFIE). For some strongly nonlinear problems, the traditional homotopy perturbation method is divergent, so we propose a modified homotopy perturbation method which is still convergent when solving the strongly nonlinear mixed VFIE. By means of this method, an algorithm is successfully established for solving the strongly nonlinear mixed VFIE. And the convergence of the algorithm is proved strictly. Finally, several examples are presented to illustrate the application of the algorithm.