Applied optimal homotopy analysis method to calculate the analytical approximation of a nonlinear jerk equation
Zheng Min-yi1,Hu Hui1,Guo Yuan-jun1, Sun Guang-yong2
1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China;2. State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha 410082, China
Abstract：An Optimal Homotopy Analysis Method is applied to calculate the approximate periods and analytical approximate periodic solutions of a third-order differential equation with cubic nonlinearities. An example shows that the accurate second-order analytical approximate periodic solution is easy obtained via Optimal Homotopy Analysis Method. When initial velocity amplitude are large, the largest percentage error of the first-order approximate period in relation to the exact one is -0.415%, and the largest percentage error of the second-order approximate period is -0.0298%. A comparison of the analytical approximate periodic solutions with the numerically exact ones shows that the first-order and second-order analytical approximate periodic solutions have very high accuracy. It demonstrates that Optimal Homotopy Analysis Method is very effective for nonlinear Jerk equation.
2012, Vol. 31 
