Homotopy Analysis Approach to Periodic Solutions of a Nonlinear Jerk Equation
FENG Shao-Dong1, CHEN Li-Qun1,2
1Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 2000722Department of Mechanics, Shanghai University, Shanghai 200444
Homotopy Analysis Approach to Periodic Solutions of a Nonlinear Jerk Equation
FENG Shao-Dong1, CHEN Li-Qun1,2
1Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 2000722Department of Mechanics, Shanghai University, Shanghai 200444
摘要The homotopy analysis method is applied to seek periodic solutions of a nonlinear jerk equation involving the third-order time-derivative. The periodic solutions can be approximated via an analytical series. An auxiliary parameter is introduced to control the convergence region of the solution series. Two numerical examples are presented to demonstrate the effectiveness of the homotopy analysis approach. The examples indicate that, by choosing a proper value of the auxiliary parameter, the first few terms in the solution series yield excellent results.
Abstract：The homotopy analysis method is applied to seek periodic solutions of a nonlinear jerk equation involving the third-order time-derivative. The periodic solutions can be approximated via an analytical series. An auxiliary parameter is introduced to control the convergence region of the solution series. Two numerical examples are presented to demonstrate the effectiveness of the homotopy analysis approach. The examples indicate that, by choosing a proper value of the auxiliary parameter, the first few terms in the solution series yield excellent results.
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2009, Vol. 26 
