Convergence of the homotopy perturbation method

The present paper is devoted to the analysis of the homotopy perturbation method. The question of convergence of the method is resolved. It is theoretically proven that under a special constraint the homotopy perturbation method converges to the exact solution of sought solution of nonlinear ordinary or partial differential equation. An error estimate is also provided. Examples clearly demonstrate, why and on what interval, the corresponding homotopy series generated by the homotopy perturbation method converges to the exact solution.