Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM

In this study, a nonlinear oscillation equation is solved using a series-based analytical method called differential transformation method (DTM). The concept of differential transformation is briefly introduced, and its application for a nonlinear oscillator is studied. The results obtained employing DTM are compared with those achieved by using two other series-based analytical techniques named variation iteration method (VIM) and homotopy perturbation method (HPM) and also an accurate numerical solution to verify the accuracy of the proposed method. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by HPM and VIM. After this verification, we analyze the effects of some physical applicable parameters to show the efficiency of DTM for this type of problems. It is shown that in most cases, DTM is accurate enough; nevertheless some modifications should be applied to enhance the abilities of this technique.