Effective approximate methods for strongly nonlinear differential equations with oscillations
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
Mathematical Sciences 2012, 6:32 doi:10.1186/2251-7456-6-32Published: 5 September 2012
This paper proposes the use of different analytical methods in obtaining approximate solutions for nonlinear differential equations with oscillations.
Three methods are considered in this paper: Lindstedt-Poincare method, the Krylov-Bogoliubov first approximate method, and the differential transform method.
Figures that are given in this paper give a strong evidence that the proposed methods are effective in handling nonlinear differential equations with oscillations.
This study reveals that the differential transform method provides a remarkable precision compared with other perturbation methods.