He's frequency formulation for nonlinear oscillators

European Journal of Physics

Volumn 28, Issue 5, 2007, Pages 923-931

  Geng, Lei ^a   Cai, Xu Chu ^a  

^a DONGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FREQUENCY ESTIMATION; NONLINEAR SYSTEMS;

CHINESE ALGORITHM; FREQUENCY FORMULATION; NONLINEAR OSCILLATORS;

OSCILLATORS (ELECTRONIC);

EID: 36048969106     PISSN: 01430807     EISSN: 13616404     Source Type: Journal    
DOI: 10.1088/0143-0807/28/5/016     Document Type: Article

References (35)

1. Beléndez A, Hernndez A, Beléndez T, Mrquez A and Neipp C 2007 An improved 'heuristic' approximation for the period of a nonlinear pendulum: linear analysis of a classical nonlinear problem Int. J. Nonlinear Sci. Numer. Simul. 8 329-34
2. Gorji M, Ganji D D and Soleimani S 2007 New application of He's homotopy perturbation method Int. J. Nonlinear Sci. Numer. Simul. 8 319-28
3. Biazar J and Ghazvini H 2007 He's variational iteration method for solving hyperbolic differential equations Int. J. Nonlinear Sci. Numer. Simul. 8 311-4
4. Sadighi A and Ganji D D 2007 Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods Int. J. Nonlinear Sci. Numer. Simul. 8 435-44
5. Tatari M and Dehghan M 2007 He's variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation Chaos Solitons Fractals 33 671-7
6. Biazar J, Eslami M and Ghazvini H 2007 Homotopy perturbation method for systems of partial differential equations Int. J. Nonlinear Sci. Numer. Simul. 8 413-8
7. He J H 1999 Variational iteration method-a kind of non-linear analytical technique: some examples Int. J. Non-Linear Mech. 34 699-708
8. Momani S and Abuasad S 2006 Application of He's variational iteration method to Helmholtz equation Chaos Solitons Fractals 27 1119-23
9. Yusufoglu E 2007 Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations Int. J. Nonlinear Sci. Numer. Simul. 8 153-8
10. He J H 2006 New interpretation of homotopy perturbation method Int. J. Mod. Phys. B 20 2561-8
11. He J H 2005 Homotopy perturbation method for bifurcation of nonlinear problems Int. J. Nonlinear Sci. Numer. Simul. 6 207-8
12. Beléndez A et al 2007 Application of the homotopy perturbation method to the nonlinear pendulum Eur. J. Phys. 28 93-104
13. Beléndez A et al 2007 Application of He's homotopy perturbation method to the Duffing-harmonic oscillator Int. J. Nonlinear Sci. Numer. Simul. 8 79-88
14. Rafei M and Ganji D D 2006 Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method Int. J. Nonlinear Sci. Numer. Simul. 7 321-8
15. zi T and Yildirim A 2007 A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities Int. J. Nonlinear Sci. Numer. Simul. 8 243-8
16. Yusufolu E 2007 Homotopy perturbation method for solving a nonlinear system of second order boundary value problems Int. J. Nonlinear Sci. Numer. Simul. 8 353-8
17. Cveticanin L 2006 Homotopy-perturbation method for pure nonlinear differential equation Chaos Solitons Fractals 30 1221-30
18. He J H 2007 Variational approach for nonlinear oscillators Chaos Solitons Fractals 34 1430-9
19. Xu L 2007 Determination of limit cycle by He's parameter-expanding method for strongly nonlinear oscillators J. Sound Vib. 302 178-84
20. Shou D H et al 2007 Application of parameter-expanding method to strongly nonlinear oscillators Int. J. Nonlinear Sci. Numer. Simul. 8 121-4
21. He J-H and Wu X-H 2006 Exp-function method for nonlinear wave equations Chaos Solitons Fractals 30 700-8
22. Zhu S-D 2007 Exp-function method for the hybrid-lattice system Int. J. Nonlinear Sci. Numer. Simul. 8 461-4
23. Zhu S-D 2007 Exp-function method for the discrete mKdV lattice Int. J. Nonlinear Sci. Numer. Simul. 8 465-8
24. He J H 2006 Some asymptotic methods for strongly nonlinear equations Int. J. Mod. Phys. B 20 1141-99
25. He J H 2006 Nonperturbative methods for strongly nonlinear problems Dissertation.de-Verlag im Internet GmbH
26. He J H 2002 Ancient Chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method Appl. Math. Mech. 23 1407-12
27. He J H 2004 Solution of nonlinear equations by an ancient Chinese algorithm Appl. Math. Comput. 151 293-7
28. Kline M 1972 Mathematical Thought from Ancient to Modern Times (New York: Oxford University Press)
29. He J H and Tang H 2005 Rebuild of King Fang 40 BC musical scales by He's inequality Appl. Math. Comput. 168 909-14
30. He J H 2004 Mysterious pi and a possible link to DNA sequencing Int. J. Nonlinear Sci. Numer. Simul. 5 263-74
31. He J H 2004 Some interpolation formulas in Chinese ancient mathematics Appl. Math. Comput. 152 367-71
32. He J H 2004 Zu-Geng's axiom vs Cavalieri's theory Appl. Math. Comput. 152 9-15
33. He J H 2004 He Chengtian's inequality and its applications Appl. Math. Comput. 151 887-91
34. Dauben J W 1998 Ancient Chinese mathematics: the Jiu Zhang Suan Shu vs Euclid's Elements. Aspects of proof and the linguistic limits of knowledge Int. J. Eng. Sci. 36 1339-59
35. Cullen C 1996 Astronomy and Mathematics in Ancient China: The Zhou bi suan jing (New York: Cambridge University Press)