Improving convergence of incremental harmonic balance method using homotopy analysis method

作     者：Yanmao Chen Jike Liu 

作者机构：State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University 800 Dongchuan Road 200240 Shanghai China Department of Mechanics Sun Yat-sen University 510275 Guangzhou China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2009年第25卷第5期

页      面：707-712页

核心收录：

学科分类：12[管理学] 083002[工学-环境工程] 1204[管理学-公共管理] 120402[管理学-社会医学与卫生事业管理(可授管理学、医学学位)] 0830[工学-环境科学与工程（可授工学、理学、农学学位）] 07[理学] 08[工学] 0837[工学-安全科学与工程] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (10772202) Doctoral Program Foundation of Ministry of Education of China (20050558032) Guangdong Province Natural Science Foundation (07003680, 05003295) 

主　　题：Incremental harmonic balance method Homotopy analysis method Initial value Convergence 

摘      要：We have deduced incremental harmonic balance an iteration scheme in the （IHB） method using the harmonic balance plus the Newton-Raphson method. Since the convergence of the iteration is dependent upon the initial values in the iteration, the convergent region is greatly restricted for some cases. In this contribution, in order to enlarge the convergent region of the IHB method, we constructed the zeroth-order deformation equation using the homotopy analysis method, in which the IHB method is employed to solve the deformation equation with an embedding parameter as the active increment. Taking the Duffing and the van der Pol equations as examples, we obtained the highly accurate solutions. Importantly, the presented approach renders a convenient way to control and adjust the convergence.