Efficient multi-step differential transform method: Theory and its application to nonlinear oscillators

•We propose an efficient method based on multi-step differential transform method.•The proposed method is suitable for solving the nonlinear oscillatory systems.•The closed-form solution for systems of nonlinear equations is presented.•The number of arithmetic operations in the proposed method is considerably reduced. In this paper, we suggest an efficient method, based on the well-known multi-step differential transform method to considerably reduce the number of arithmetic operations of differential transform method. The proposed method is heavily depended on the solution of two nonlinear systems which are exactly solved and the closed-form expressions are derived, fortunately. The present method is suitable for solving the governing equations of oscillatory systems. This fact is thoroughly shown by several nonlinear numerical examples. Moreover, the number of arithmetic operations is calculated for all methods implemented in the article, i.e., the proposed method and two previous methods, and it is clearly illustrated that the present method is really efficient.