Effective approximate methods for strongly nonlinear differential equations with oscillations

Purpose: This paper proposes the use of different analytical methods in obtaining approximate solutions for nonlinear differential equations with oscillations. Methods: Three methods are considered in this paper: Lindstedt-Poincare method, the Krylov-Bogoliubov first approximate method, and the differential transform method. Results: Figures that are given in this paper give a strong evidence that the proposed methods are effective in handling nonlinear differential equations with oscillations. Conclusions: This study reveals that the differential transform method provides a remarkable precision compared with other perturbation methods.