Generating the periodic solutions for forcing van der Pol oscillators by the Iteration Perturbation method

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 4, 2009, Pages 1984-1989

  Öziş, Turgut ^a   Yildirim, Ahmet ^a  

^a EGE UNIVERSITY   (Turkey)

Author keywords

Forcing nonlinear oscillators; Nonlinear systems; van der Pol's equation

Indexed keywords

BIPED LOCOMOTION; CIRCUIT OSCILLATIONS; HELIUM; ITERATIVE METHODS; LINEARIZATION; LYAPUNOV METHODS; NONLINEAR SYSTEMS; OSCILLATORS (MECHANICAL); PERTURBATION TECHNIQUES; SOLITONS;

CHAOS SOLITONS; FORCING NONLINEAR OSCILLATORS; FORCING TERMS; LIMIT CYCLES; NON-LINEAR PROBLEMS; PERIODIC SOLUTIONS; PERTURBATION METHODS; PERTURBATIVE METHODS; STRONGLY NONLINEAR; VAN DER POL OSCILLATORS; VAN DER POL'S EQUATION;

NONLINEAR EQUATIONS;

EID: 61749091924     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.03.005     Document Type: Article

References (31)

1. Nayfeh A.H. Problems in Perturbations (1985), Wiley, New York
2. He J.H. Some asymptotic methods for strongly nonlinear equations. Internat. J. Modern Phys. B 10 (2006) 1141-1199
3. J.H. He, Non-perturbative methods for strongly nonlinear problems, Dissertation. de-Verlag im Internet GmbH, 2006
4. He J.H. Determination of limit cycles for strongly nonlinear oscillators. Phys. Rev. Lett 90 17 (2003) 174301
5. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. Determination of frequency-amplitude relation for duffing- harmonic oscillator by the energy balance method. Chaos Solitons Fractals 54 7-8 (2007) 1184-1187
6. He J.H. Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng 178 (1999) 257-262
7. He J.H. Homotopy perturbation method: A new nonlinear analytical technique. Appl. Math. Comput. 135 (2003) 73-79
8. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Non-linear Sci. Numer. Simul. 6 2 (2005) 207-208
9. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity. Chaos Solitons Fractals 34 3 (2007) 989-991
10. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. A comparative study of he's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities. Int. J. Non-linear Sci. Numer. Simul. 8 2 (2007) 243-248
11. Yi{dotless}ldi{dotless}ri{dotless}m A., and Öziş T. Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method. Phys. Lett. A 369 1-2 (2007) 70-76
12. Belendez A., Hernandez A., Belendez T., Fernandez E., Alvarez M.L., and Neipp C. Application of He's homotopy perturbation method to the duffing-harmonic oscillator. Int. J. Non-linear Sci. Numer. Simul. 8 1 (2007) 79-88
13. He J.H. Variational iteration method: a kind of nonlinear analytical technique: Some examples. Internat. J. Non-Linear Mech. 34 4 (1999) 699-708
14. Marinca V. An approximate solution for 1-D weakly nonlinear oscillations. Int. J. Non-linear Sci. Numer. Simul. 3 (2002) 107-120
15. 1 / 3 force by He's variational iteration method. J. Sound Vibration 306 1-2 (2007) 372-376
16. He J.H. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part I: Expansion of a constant. Int. J. Non-Linear Mech. 37 2 (2002) 309-314
17. He J.H. Modified Lindstedt-Poincaré methods for some strongly nonlinear oscillations:Part II: A new transformation. Int. J. Non-Linear Mech. 37 2 (2002) 315-320
18. 1 / 3 force by He's modified Lindstedt-Poincaré method. J. Sound Vibration 301 1-2 (2007) 415-419
19. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. Determination of limit cycles by modified straightforward expansion for nonlinear oscillators. Chaos Solitons Fractals 32 2 (2007) 445-448
20. Liu H.M. Variational approach to nonlinear electrochemical system. Int. J. Non-linear Sci. Numer. Simul. 5 1 (2004) 95-96
21. He J.H. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos Solitons Fractals 19 4 (2004) 847-851
22. Xu L. He's parameter-expanding method for strongly nonlinear oscillators. J. Comput. Appl. Math. 207 1 (2007) 148-154
23. Shou D.H., and He J.H. Application of parameter-expanding method to strongly nonlinear oscillators. Int. J. Non-linear Sci. Numer. Simul 8 1 (2007) 121-124
24. Belendez A., Hernandez A., Belendez T., Marquez A., and Neipp C. An improved 'heuristic' approximation for the period of a nonlinear pendulum: Linear analysis of a classical nonlinear problem. J. Non-linear Sci. Numer. Simul 8 3 (2007) 329-334
25. A. Belendez, D.I. Mendez, T. Belendez, A. Hernandez, M.L. Alvarez, Harmonic balance approaches to the nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable, J. Sound Vibration (2008), doi:10.1016/j.jsv.2008.01.021
26. Abdusalam H.A. On an improved complex tan h-function method. Int. J. Non-linear Sci. Numer. Simul. 6 2 (2005) 99-106
27. Abbasy T.A., El-Tawil M.A., and Saleh H.K. The solution of KdV and mKdV equations using Adomian Pade approximation. Int. J. Non-linear Sci. Numer. Simul. 5 4 (2004) 327-340
28. Geng L., and Cai X.C. He's frequency formulation for nonlinear oscillators. European J. Phys. 28 5 (2007) 923-931
29. He J.H. Iteration perturbation method for strongly nonlinear oscillators. J. Vibration Control 7 5 (2001) 631-642
30. He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos Solitons Fractals 26 (2005) 827-833
31. Abd El-Latif G.M. Parametric excitation for forcing van der Pol oscillator. Appl. Math. Comput. 147 (2004) 255-265