The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system

Chaos, Solitons and Fractals

Volumn 40, Issue 4, 2009, Pages 1929-1937

  Chowdhury, M S H ^a   Hashim, I ^a   Momani, S ^b  

^a UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

^b QATAR UNIVERSITY   (Qatar)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; RUNGE KUTTA METHODS;

APPROXIMATE SOLUTION; FOURTH-ORDER RUNGE-KUTTA; HOMOTOPY PERTURBATION METHOD (HPM); LORENZ SYSTEM; NUMERICAL COMPARISON; TIME STEP;

PERTURBATION TECHNIQUES;

EID: 65449158498     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.09.073     Document Type: Article

References (23)

1. Abdulaziz O., Noor N.F.M., Hashim I., and Noorani M.S.M. Further accuracy tests on Adomian decomposition method for chaotic systems. Chaos Solitons & Fractals 36 5 (2008) 1405-1411
2. Adomian G. Nonlinear stochastics systems theory and application to physics (1988), Reidel, Dordrecht
3. Chowdhury M.S.H., and Hashim I. Solutions of a class of singular second-order IVPs by homotopy-perturbation method. Phys Lett A 365 (2007) 439-447
4. Chowdhury M.S.H., Hashim I., and Abdulaziz O. Application of homotopy-perturbation method to nonlinear population dynamics models. Phys Lett A 368 (2007) 251-258
5. Chowdhury MSH, Hashim I. Solutions of time-dependent Emden-Fowler type equations by homotopy-perturbation method. Phys Lett A, doi:10.1016/j.physleta.2007.04.020.
6. Chowdhury MSH, Hashim I. Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations. Chaos Solitons & Fractals, in press.
7. Gill T.S., Singh A., Kaur H., Saini N.S., and Bala P. Ion-acoustic solitons in weakly relativistic plasma containing electron-positron and ion. Phys Lett A 361 4-5 (2007) 364-367
8. Guellal S., Grimalt P., and Cherruault Y. Numerical study of Lorenz's equation by the Adomian method. Comput Math Appl 33 (1997) 25-29
9. Hashim I., Noorani M.S.M., Ahmad R., Bakar S.A., Ismail E.S., and Zakaria A.M. Accuracy of the Adomian decomposition method applied to the Lorenz system. Chaos Solitons & Fractals 28 (2006) 1149-1158
10. He J.H. Approximate analytical solution of Blasius' equation. Commun Nonlinear Sci Numer Simul 3 (1998) 260-263
11. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int J Non-Linear Mech 35 (2000) 37-43
12. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos Solitons & Fractals 26 (2005) 695-700
13. He J.H. Non-perturbative methods for strongly nonlinear problems (2006), Die Deutsche bibliothek, Germany
14. He J.H. Some asymptotic methods for strongly nonlinear equations. Int J Mod Phys B 20 10 (2006) 1141-1199
15. He J.H. Homotopy perturbation method for solving boundary value problems. Phys Lett A 350 (2006) 87-88
16. Lorenz E.N. Deterministic nonperiodic flow. J Atmospheric Sci 20 2 (1963) 130-141
17. Momani S, Odibat Z. Comparison between homotopy perturbation method and the variational iteration method for linear fractional partial differential equations. Computers Math Appl, in press.
18. Momani S., and Odibat Z. Homotopy perturbation method for nonlinear partial differential equations of fractional order. Phys Lett A 365 (2007) 345-350
19. Noor M.A., and Mohyud-Din S.T. An efficient algorithm for solving fifth-order boundary value problems. Math Comput Model 45 7-8 (2007) 954-964
20. Noorani M.S.M., Hashim I., Ahmad R., Bakar S.A., Ismail E.S., and Zakaria A.M. Comparing numerical methods for the solutions of the Chen system. Chaos Solitons & Fractals 32 (2007) 1296-1304
21. Odibat Z, Momani S. Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order. Chaos Solitons & Fractals, doi:10.1016/j.chaos.2006.06.041.
22. Shakeri F., and Dehghan M. Inverse problem of diffusion equation by He's homotopy perturbation method. Phys Scr 75 4 (2007) 551-556
23. Zhang L.N., and He J.H. Homotopy perturbation method for the solution of the electrostatic potential differential equation. Math Prob Eng (2006) 83878