应用优化的同伦分析法求解非线性Jerk方程

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (5) : 21-25.

论文

应用优化的同伦分析法求解非线性Jerk方程

郑敏毅1，胡辉1，郭源君1，孙光永2

作者信息 +

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

Author information +

文章历史 +

摘要

应用优化的同伦分析法计算了具有三次非线性项的三阶微分方程(Jerk)的近似周期和近似解析周期解。文中给出一个算例说明由优化的同伦分析法可以容易得到精确的二阶近似周期解。当初速度比较大时，一阶近似周期与精确周期的百分比误差为-0.415%，而二阶近似周期与精确周期的百分比误差为-0.0298%。与数值方法给出的“精确”周期解比较，一阶近似解析周期解和二阶近似周期解的精度很高。这个说明同伦分析法对求解非线性Jerk方程非常有效

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.

导出引用

郑敏毅;胡辉;郭源君;孙光永. 应用优化的同伦分析法求解非线性Jerk方程[J]. 振动与冲击, 2012, 31(5): 21-25

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