Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

被引：58
作者：
Akbari M.R. [1 ]
Ganji D.D. [2 ]
Majidian A. [3 ]
Ahmadi A.R. [3 ]
机构：
[1] Department of Civil Engineering and Chemical Engineering, University of Tehran, Tehran
[2] Department of Mechanical Engineering, Babol University of Technology, Babol
[3] Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari
来源：
Frontiers of Mechanical Engineering | 2014年 / 9卷 / 2期
关键词：
Algebraic Method (AGM); Angular Frequency; Duffing; Rayleigh; Vanderpol;
D O I：
10.1007/s11465-014-0288-8
中图分类号：
学科分类号：
摘要：
In the present paper, three complicated nonlinear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method (AGM). Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method (Runge-Kutte 4th). Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems. © 2014 Higher Education Press and Springer-Verlag Berlin Heidelberg.
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页码：177 / 190
页数：13
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