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

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. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.