A reliable modification of the homotopy perturbation method for differential and integral equations

In this paper, a new reliable modification of the homotopy perturbation method (HPM) is introduced and applied to the differential and integral equations. A comparative study between the modified homotopy method (MHPM) and the standard HPM is conducted. The efficiency of the modified technique is examined by several illustrative examples. In all cases of differential and integral equations, the modified HPM yields the exact solutions in two iterations only.