Application of homotopy-perturbation to non-linear partial differential equations

Chaos, Solitons and Fractals

Volumn 40, Issue 1, 2009, Pages 221-228

  Cveticanin, L ^a  

^a UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

APPROXIMATE SOLUTION; HE'S HOMOTOPY PERTURBATION METHODS; HOMOTOPIES; LONGITUDINAL VIBRATIONS; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; VARIATIONAL ITERATION METHOD;

PERTURBATION TECHNIQUES;

EID: 64849106150     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.07.053     Document Type: Article

References (36)

1. Nayfeh A.H., and Nayfeh S.A. Nonlinear normal modes of a continuous system with quadratic nonlinearities. ASME J Vibr Acoust 117 (1995) 477-481
2. Shaw S.W. An invariant manifold approach to nonlinear normal modes of oscillation. J Nonlin Sci 4 (1994) 419-448
3. Shaw S.W., and Pierre C. Normal modes of vibration for nonlinear continuous systems. J Sound Vib 169 (1994) 319-347
4. Ling F.H., and Wu X.X. Fast Galerkin method and its application to determining periodic solutions of non-linear oscillators. Int J Non-lin Mech 22 (1987) 89-98
5. Lewandowski R. Solutions with bifurcation points for free vibrations of beams: an analytical approach. J Sound Vib 177 (1994) 239-249
6. von Wagner U. Non-linear longitudinal vibrations of pezoceramics excited by weak electric fields. Int J Non-Lin Mech 38 (2003) 565-574
7. von Wagner U. Non-linear longitudinal vibrations of non-slender piezoceramic rods. Int J Non-Lin Mech 39 (2004) 673-688
8. Cveticanin L., and Uzelac Z. Nonlinear longitudinal vibrations of a rod. J Vib Contr 5 (1999) 827-849
9. Lacarbonara W. Direct treatment and discretizations of non-linear spatially continuous systems. J Sound Vib 221 (1999) 849-866
10. Nayfeh A.H., and Mook D.T. Nonlinear oscillations (1979), John Wiley & Sons, New York
11. Lau S.L., Cheung Y.K., Cing S., and Wu X.X. An alternative perturbation procedure of multiple scales for nonlinear dynamical systems, ASME. J Appl Mech 56 (1989) 667-675
12. Boertjens G.J., and van Horssen W.T. On interaction of oscillation modes for a weakly non-linear undamped elastic beam with an external force. J Sound Vib 235 (2000) 201-217
13. Adrianov I.V., and Danishevskyy V.V. Asymptotic approach for non-linear periodical vibrations of continuous structures. J Sound Vib 249 (2002) 465-481
14. He J.-H. Application of homotopy perturbation method to a nonlinear wave equations. Chaos, Solitons & Fractals 26 (2005) 695-700
15. El-Shahed M. Application of He's homotopy perturbation method to a Volterra's integro-differential equation. Int J Nonlin Sci Numer Simul 6 (2005) 163-167
16. He J.-H. Homotopy perturbation technique. Comput Meth Appl Mech Eng 178 (1999) 257-262
17. He J.-H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int J Non-Lin Mech 35 (2000) 37-43
18. He J.-H. Homotopy perturbation method: a new nonlinear analytical technique. Appl Math Comput 135 (2003) 73-79
19. He J.-H. Asymptotology by homotopy perturbation method. Appl Math Comput 156 (2004) 591-596
20. He J.-H. Comparison of homotopy perturbation method and homotopy analysis method. Appl Math Comput 156 (2004) 527-539
21. Golbabai A., and Keramati B. Modified homotopy perturbation method for solving Fredholm integral equations. Chaos, Solitons & Fractals 37 (2008) 1528-1537
22. Abbasbandy S. Application of He's homotopy perturbation method to functional integral equations. Chaos, Solitons & Fractals 31 (2007) 1243-1247
23. Biazar J., and Ghazvini H. He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind. Chaos, Solitons & Fractals 38 (2008) 731-742
24. He J.-H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals 26 (2005) 695-700
25. Tan Y., Xu H., and Liao S.-J. Explicit series solution of travelling waves with a front of Fischer equation. Chaos, Solitons & Fractals 31 (2007) 462-472
26. He J.-H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl Math Comput 151 (2004) 287-292
27. Cveticanin L. The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic non-linearity. J Sound Vib 285 (2005) 1171-1179
28. Cveticanin L. Homotopy-perturbation method for pure non-linear differential equation. Chaos, Solitons & Fractals 30 (2006) 1221-1230
29. Ozis T., and Yildirims A. A note on He's homotopy-perturbation method for van der Pol oscillator with very strong nonlinearity. Chaos, Solitons & Fractals 34 (2007) 989-991
30. He J.-H. Variational iteration method - a kind of non-linear analytical technique: Some examples. Int J Non-Lin Mech 34 (1999) 699-708
31. He J.-H. Variational iteration method for autonomous ordinary differential systems. Appl Math Comput 114 (2000) 115-123
32. Momani S., and Abuasad S. Application of He's variational iteration method to Helmholtz equation. Chaos, Solitons & Fractals 27 (2006) 1119-1123
33. He J.-H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Meth Appl Mech Eng 167 (1998) 57-68
34. Odibat Z., and Momani S. Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order. Chaos, Solitons & Fractals 36 (2008) 167-174
35. Wang Q. Homotopy perturbation method for fractional KdV-Burgers equation. Chaos, Solitons & Fractals 35 (2008) 843-850
36. He J.-H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput Meth Appl Mech Eng 167 (1998) 69-73