Homotopy perturbation method with rank upgrading technique for the superior nonlinear oscillation

Abstract

In the present work, the rank upgrade method is suggested to obtain a periodic approximate solution for some complicated nonlinear problems. The method depends on obtaining an equivalent simple equation having a polynomial of nonlinearity without using the Taylor expansion. The solution process is extremely simple, as simple as that by the traditional perturbation method. This approach yields a highly accurate in obtaining analyticity approximate solution for the superior nonlinear oscillation. The results are attractive and valid for both weakly and strongly nonlinear cases.