Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method

Chaos, Solitons and Fractals

Volumn 39, Issue 4, 2009, Pages 1744-1752

  Allan, Fathi M ^a  

^a UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

ANALYTIC APPROACH; ANALYTIC SOLUTION; BIFURCATION PARAMETER; CHAOTIC DYNAMICAL SYSTEMS; HOMOTOPY ANALYSIS METHODS; NUMERICAL TECHNIQUES; SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS; TRANSITION REGIONS;

RUNGE KUTTA METHODS;

EID: 63449140515     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.06.116     Document Type: Article

References (32)

1. Allan F., and Al-Khaled K. An approximation of the analytic solution of the shock wave equation. J Comp Appl Math 192 2 (2006) 301-309
2. Al-Khaled K., and Allan F. Decomposition method for solving nonlinear integro-differential equations. J Appl Math Comput 19 1-2 (2005) 415-425
3. Allan F. On the analytic solution of non-linear boundary value problem with infinite domain. In: Proceedings of the 6th annual conference of UAEU. April 2005.
4. Allan F.M., and Syam M.I. On the analytic solutions of the nonhomogeneous Blasius problem. J Comput Appl Math 182 2 (2005) 362-371
5. Allan F.M. Derivation of the Adomian decomposition method using the Homotopy analysis method. Appl Math Comput 190 1 (2007) 6-14
6. Biazar J., and Montazeri R. A computational method for solution of the prey and predator problem. Appl Math Comput 163 (2005) 841-847
7. Dadfar M.B., Geer J., and Andersen C.M. Perturbation analysis of the limit cycle of the free Van der Pol equation. SIAM J Appl Math 44 5 (1984)
8. He J.H. Variational iteration method: a kind of nonlinear analytical technique: some examples. Int Non-Linear Mech 344 (1999) 699-708
9. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl Math Comput 114 2,3 (2000) 115-123
10. He J.H. Commun Nonlinear Sci Number Simul 3 (2002) 107-120
11. He J.H. Homotopy perturbation method: a new nonlinear technique. Appl Math Comput 135 (2003) 73-79
12. He J.H. Application of Homotopy perturbation method to nonlinear wave equation. Chaos, Solitons & Fractals 26 (2005) 695-700
13. He J.H. Exp-function method for nonlinear wave equation. Chaos, Solitons & Fractals 26 (2006) 700-708
14. He J.H. Variational approach for nonlinear oscillators. Chaos, Solitons & Fractals 34 5 (2007) 1430-1439
15. He J.H. Some asymptotic methods for strongly nonlinear equations. Int J Mod Phys B 20 10 (2006) 1141-1199
16. Liao S.J. An approximate solution technique not depending on small parameters: a special example. Int J Non-Linear Mech 30 3 (1995) 371-380
17. Liao S.J. An approximate solution technique not depending on small parameters (Part 2): an application in fluid mechanics. Int J Non-Linear Mech 32 5 (1997) 815-822
18. Liao S.J. Numerically solving non-linear problems by the Homotopy analysis method. Computational Mechanics 20 (1997) 530-540
19. Lorenz E.N. Deterministic nonperiodic flow. J Atmos Sci 20 2 (1963) 130-141
20. Nayfeh H.A., and Mook D.T. Non-linear oscillations (1979), Wiley, New York
21. Olek S. An accurate solution to the multispecies Lotka-Volterra equations. SIAM Rev 36 3 (1994) 480-488
22. Sparrow C. The Lorenz equations: bifurcations, chaos, and strange attractors (1982), Springer-Verlag, New York
23. Tan Y., Xu H., and Liao S.J. Explicit series solution of traveling waves with a front of Fisher equation. Chaos, Solitons & Fractals 31 (2007) 462-472
24. Wazwaz A.M. Exact solutions with solitons and periodic structures for the Zakharov-Kuznetsov (ZK) equation and its modified form. Commun Nonlinear Sci Numer Simul 10 (2005) 597-606
25. Wazwaz A.M. A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations. Appl Math Comput 181 2 (2006) 1703-1712
26. Wazwaz A.M. A comparison between the variational iteration method and Adomian decomposition method. J Comp Appl Math 207 1 (2007) 129-136
27. Wazwaz A.M. The modified decomposition method and Padé approximants for a boundary layer equation in unbounded domain. Appl Math Comput 177 2 (2006) 737-744
28. Wazwaz A.M. The modified decomposition method for analytic treatment of differential equations. Appl Math Comput 173 1 (2006) 165-176
29. Wazwaz A.M. Adomian decomposition method for a reliable treatment of the Bratu-type equations. Appl Math Comput 166 3 (2005) 652-663
30. Wazwaz A.M. Adomian decomposition method for a reliable treatment of the Emden-Fowler equation. Appl Math Comput 161 2 (2005) 543-560
31. Wu W., and Liao S.J. Solving solitary waves with discontinuity by means of Homotopy analysis method. Chaos, Solitons & Fractals 26 (2005) 177-185
32. Wu Y., Wang C., and Liao S.J. Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method. Chaos, Solitons & Fractals 23 (2005) 1733-1740