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| 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 |
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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.
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Received: 10 December 2010
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Corresponding Authors:
Zheng Min-yi
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2012, Vol. 31 
