Inconsistent Sumudu Transform Series Decomposition Method for Asymmetric Nonlinear Oscillations

Abstract

The sumudu transform series decomposition method (STSDM) is claimed to be a powerful technique for solving problems in science and engineering fields. It provides diverging series solution similar to that of differential transform method (DTM). To capture the periodic solution, the concepts of modified DTM are utilized by applying Laplace transformation, pade’s approximant and inverse Laplace transformation. Many researchers have examined the adequacy of STSDM considering a standard Duffing equation of motion having symmetric oscillations. This paper examines the applicability of STSDM in obtaining the asymmetric oscillations of a simple Helmholtz nonlinear equation of motion and confirms its inconsistency in differentiating the asymmetrical oscillation behavior and the non-periodic nature of the models.