Solution procedure of residue harmonic balance method and its applications
Solution procedure of residue harmonic balance method and its applications作者机构：School of Mathematics and Statistics Taishan University Department of Civil and Architectural Engineering City University of Hong Kong
出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)
年 卷 期：2014年第57卷第8期
页 面：1581-1591页
核心收录：
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金：supported by the Natural Science Foundation of Shandong Province China(Grant Nos.ZR2011AQ022 and ZR2012AL03)
主 题：residue harmonic balance accurate approximation fractional ordinary differential system delay ordinary differential system
摘 要：This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential *** this solution procedure,no small parameter is *** harmonic residue of balance equation is separated in two parts at each *** first part has the same number of Fourier terms as the present order of approximation and the remaining part is used in the subsequent *** corrections are governed by linear ordinary differential equation so that they can be solved easily by means of harmonic balance method *** kinds of different differential equations involving general,fractional and delay ordinary differential systems are given as numerical examples *** accurate limited cycle frequency and amplitude are *** results match well with the exact solutions or numerical solutions for a wide range of control *** with those available shows that the residue harmonic balance solution procedure is very effective for these autonomous differential ***,the present method works not only in predicting the amplitude but also the frequency of bifurcated period solution for delay ordinary differential equation.
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