Modified Homotopy Perturbation Method for Certain Strongly Nonlinear Oscillators
NIU Yao-Bin** , WANG Zhong-Wei, DONG Si-Wei
College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha 410073
Modified Homotopy Perturbation Method for Certain Strongly Nonlinear Oscillators
NIU Yao-Bin** , WANG Zhong-Wei, DONG Si-Wei
College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha 410073
Abstract ：A new modified homotopy perturbation method is presented for strongly non-linear oscillation by coupling the homotopy perturbation method and the modified Lindstedt–Poincaré method. The advantage of this method is that it does not need a small parameter in the physical system as in He's homotopy perturbation method, and the accuracy is greatly improved. Some examples are tested, and the obtained results show that the current method is very effective and convenient for solving strongly nonlinear oscillators.
Key words ：
05.45.-a
03.65.Ge
收稿日期: 2011-11-07
出版日期: 2012-05-31
:
05.45.-a
(Nonlinear dynamics and chaos)
03.65.Ge
(Solutions of wave equations: bound states)
[1] He J H 1999 Int. J. Nonlinear Mech. 34 699 [2] Odibat Z M and Momani S 2006 Int. J. Non-linear Sci. Numer. Simul. 7 27 [3] Momani S and Abuasad S 2006 Chaos Solitons Fractals 27 1119 [4] Xu L 2007 J. Comput. Appl. Math. 207 148 [5] He J H 2006 Int. J. Mod. Phys. B 20 1141 [6] Darvishi M T, Karami A and Byeong C S 2008 Phys. Lett. A 372 5381 [7] He J H 2001 Int. J. Nonlinear Sci. Numer. Simul. 2 257 [8] Liu H M 2005 Chaos Solitons Fractals 23 577 [9] He J H 2002 Int. J. Nonlinear Mech. 37 309 [10] He J H 2002 Int. J. Nonlinear Mech. 37 315 [11] He J H 2001 Int. J. Nonlinear Sci. Numer. Simul. 2 317 [12] Cheung Y K, Chen S H and Lau S L 1991 Int. J. Nonlinear Mech. 26 367 [13] Zhang Q C, Wang W and Li W Y 2008 Chin. Phys. Lett. 25 1905 [14] Gottlieb H P W 2006 J. Sound Vib. 297 243 [15] Itovich G R and Moiola J L 2005 Chaos Solitons Fractals 27 647 [16] Belendez A 2007 J. Sound Vib. 302 1018 [17] Hu H and Tang J H 2006 J. Sound Vib. 294 637 [18] He J H 1999 Comput. Methods Appl. Mech. Engin. 178 257 [19] Cveticanin L 2006 Chaos Solitons Fractals 30 1221 [20] He J H 2006 Int. J. Mod. Phys. B 20 2561 [21] Shou D H 2007 Int. J. Nonlinear Sci. Numer. Simul 8 121 [22] Belendez A, Pascual C and Gallego S 2007 Phys. Lett. A 371 421 [23] He J H 2000 Int. J. Nonlinear Mech. 35 37 [24] He J H 2004 Appl. Math. Comput. 151 287 [25] Golbabai A and Javidi M 2007 Appl. Math. Comput. 190 1409 [26] He J H 2004 Appl. Math. Comput. 156 591 [27] He J H 2006 Phys. Lett. A 350 87 [28] He J H 2005 Chaos Solitons Fractals 26 827 [29] Nayfeh A H 1981 Introduction to Perturbation Techniques (New York: Wiley)[30] He J H 2000 J. Sound Vib. 229 1257 [31] Lai S K, Lim C W, Wu B S, Wang C, Zeng Q C and He X F 2009 Appl. Math. Modeling 33 852 [32] Guo Z J, Leung A Y T and Yang H X 2011 Appl. Math. Modeling 35 1717 [33] Ganji D D, Gorji M, Soleimani S and Esmaeilpour M 2009 J. Zhejiang Univ. Sci. A 10 1263
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2012, Vol. 29 
