Application of the modified frequency formulation to a nonlinear oscillator

Computers and Mathematics with Applications

Volumn 61, Issue 8, 2011, Pages 2237-2240

  Cai, Xu Chu ^a   Liu, Jun Fang ^a  

^a DONGHUA UNIVERSITY   (China)

Author keywords

Ancient Chinese mathematics; He's frequency formulation; Nonlinear oscillator

Indexed keywords

ANCIENT CHINESE MATHEMATICS; DUFFING OSCILLATOR; GENERAL APPROACH; HE'S FREQUENCY FORMULATION; LINEAR OSCILLATOR; NON-LINEAR OSCILLATORS; SOLUTION PROCEDURE;

OSCILLATORS (ELECTRONIC);

OSCILLATORS (MECHANICAL);

EID: 79953734251     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.09.025     Document Type: Article

References (22)

1. S.T. Mohyud-Din, M.A. Noor, and K.I. Noor Parameter-expansion techniques for strongly nonlinear oscillators Int. J. Nonlinear Sci. Numer. 10 2009 581 583
2. S.S. Ganji, D.D. Ganji, and S. Karimpour Applications of He's homotopy perturbation method to obtain second-order approximations of the coupled two-degree-of-freedom systems Int. J. Nonlinear Sci. Numer. 10 2009 305 314
3. S. Momani, G.H. Erjaee, and M.H. Alnasr The modified homotopy perturbation method for solving strongly nonlinear oscillators Comput. Math. Appl. 58 2009 2209 2220
4. A. Belendez Homotopy perturbation method for a conservative x(1/3) force nonlinear oscillator Comput. Math. Appl. 58 2009 2267 2273
5. J.H. He Maxmin approach to nonlinear oscillators Int. J. Nonlinear Sci. Numer. 9 2008 207 210
6. S.A. Demirbag, and M.O. Kaya Application of He's maxmin approach to a generalized nonlinear discontinuity equation Int. J. Nonlinear. Sci. Numer. 11 2010 269 272
7. D.Q. Zeng, and Y.Y. Lee Analysis of strongly nonlinear oscillator using the maxmin approach Int. J. Nonlinear Sci. Numer. 10 2009 1361 1368
8. H.L. Zhang Periodic solutions for some strongly nonlinear oscillations by He's energy balance method Comput. Math. Appl. 58 2009 2480 2485
9. H.L. Zhang, Y.G. Xu, and J.R. Chang Application of He's energy balance method to a nonlinear oscillator with discontinuity Int. J. Nonlinear Sci. Numer 10 2009 207 214
10. G.A. Afrouzi, D.D. Ganji, and R.A. Talarposhti He's energy balance method for nonlinear oscillators with discontinuities Int. J. Nonlinear Sci. Numer 10 2009 301 304
11. J.H. He Some asymptotic methods for strongly nonlinear equations Internat. J. Modern Phys. B. 20 2006 1141 1199
12. L. Geng, and X.C. Cai He's frequency formulation for nonlinear oscillators Eur. J. Phys. 28 2007 923 931 (Pubitemid 350092681)
13. J.H. He Comment on He's frequency formulation for nonlinear oscillators Eur. J. Phys. 29 4 2008 L19 L22
14. J.H. He An improved amplitudefrequency formulation for nonlinear oscillators Int. J. Nonlinear Sci. Numer 9 2008 211 212
15. J.H. He An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering Internat. J. Modern Phys. B 22 2008 3487 3578
16. X.C. Cai, and W.Y. Wu He's frequency formulation for the relativistic harmonic oscillator Comput. Math. Appl. 58 2009 2358 2359
17. H.L. Zhang Application of He's amplitudefrequency formulation to a nonlinear oscillator with discontinuity Comput. Math. Appl. 58 2009 2197 2198
18. Y.N. Zhang, F. Xu, and L.L. Deng Exact solution for nonlinear Schrodinger equation by He's frequency formulation Comput. Math. Appl. 58 2009 2449 2451
19. J. Fan He's frequencyamplitude formulation for the Duffing harmonic oscillator Comput. Math. Appl. 58 2009 2473 2476
20. L. Zhao He's frequencyamplitude formulation for nonlinear oscillators with an irrational force Comput. Math. Appl. 58 2009 2477 2479
21. Z.F. Ren, G.Q. Liu, and Y.X. Kang Application of He's amplitudefrequency formulation to nonlinear oscillators with discontinuities Phys. Script. 80 2009 045003
22. J.H. He, G.C. Wu, and F. Austin The variational iteration method which should be followed Nonlinear Sci. Lett. A 1 2010 1 30