Applied optimal homotopy analysis method to calculate the analytical approximation of a nonlinear jerk equation

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (5) : 21-25.

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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

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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.

Key words

nonlinear jerk equation / approximate periodic solution / harmonic balance / perturbation / optimal homotopy analysis method

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Zheng Min-yi;Hu Hui;Guo Yuan-jun;Sun Guang-yong. Applied optimal homotopy analysis method to calculate the analytical approximation of a nonlinear jerk equation[J]. Journal of Vibration and Shock, 2012, 31(5): 21-25