Study on nonlinear Jeffery-Hamel flow by He's semi-analytical methods and comparison with numerical results

Computers and Mathematics with Applications

Volumn 58, Issue 11-12, 2009, Pages 2107-2116

  Ganji, Z Z ^a   Ganji, D D ^a   Esmaeilpour, M ^a  

^a BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

He's Homotopy perturbation method (HPM); He's variational iteration Method (VIM); Nonlinear ordinary differential equation of Jeffery Hamel flows

Indexed keywords

HE'S HOMOTOPY PERTURBATION METHOD (HPM); HE'S VARIATIONAL ITERATION METHOD (VIM); HOMOTOPY PERTURBATION METHOD; NONLINEAR ORDINARY DIFFERENTIAL EQUATION OF JEFFERY-HAMEL FLOWS; NONLINEAR PROBLEMS; NUMERICAL RESULTS; NUMERICAL SOLUTION; SEMI-ANALYTICAL METHODS; SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS; VARIATIONAL ITERATION METHOD;

HELIUM; LINEARIZATION; NONLINEAR EQUATIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; OSCILLATORS (MECHANICAL); PERTURBATION TECHNIQUES;

ITERATIVE METHODS;

EID: 70350574078     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.03.044     Document Type: Article

References (36)

1. Jeffery G.B. The two-dimensional steady motion of a viscous fluid. Phil. Mag. 6 (1915) 455-465
2. Hamel G. Spiralförmige Bewgungen Zäher Flüssigkeiten. Jahresber. Deutsch. Math.-Verein. 25 (1916) 34-60
3. Rosenhead L. The steady two-dimensional radial flow of viscous fluid between two inclined plane walls. Proc. R. Soc. A 175 (1940) 436-467
4. Batchelor K. An Introduction to Fluid Dynamics (1967), Cambridge University Press
5. Reza M. Sadri, Channel entrance flow, Ph.D. Thesis, Department of Mechanical Engineering, The University of Western Ontario, 1997
6. Sobey I.J., and Drazin PG. Bifurcations of two-dimensional channel flows. J. Fluid Mech. 171 (1986) 263-287
7. Hamadiche M., Scott J., and Jeandel D. Temporal stability of Jeffery-Hamel flow. J. Fluid Mech. 268 (1994) 71-88
8. Fraenkel L.E. Laminar flow in symmetrical channels with slightly curved walls. I: On the Jeffery-Hamel solutions for flow between plane walls. Proc. R. Soc. Lond. A 267 (1962) 119-138
9. Makinde O.D., and Mhone P.Y. Hermite-Padé approximation approach to MHD Jeffery-Hamel flows. Appl. Math. Comput. 181 (2006) 966-972
10. Schlichting H. Boundary-layer Theory (2000), McGraw-Hill Press, New York
11. Rathy R.K. An Introduction to Fluid Dynamics (1976), Oxford and IBH Pl, New Delhi
12. McAlpine A., and Drazin P.G. On the spatio-temporal development of small perturbations of Jeffery-Hamel flows. Fluid Dyn. Res. 22 (1998) 123-138
13. He J.H. Variational iteration method-A kind of non-linear analytical technique: Some examples. Int. J. Non-Linear Mech. 34 (1999) 699-708
14. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 (2000) 115-123
15. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Solitons Fractals 29 (2006) 108-113
16. He J.H. Variational iteration method-Some recent results and new interpretations. J. Comput. Appl. Math. 207 (2007) 3-17
17. He J.H. Homotopy perturbation technique. Comput. Methods Appl. Mech. Engrg. 178 (1999) 257-262
18. He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int. J. Non-Linear Mech. 35 (2000) 37-43
19. He J.H. Homotopy perturbation method: A new nonlinear analytical technique. Appl. Math. Comput. 135 (2003) 73-79
20. He J.H., and Wu X.H. Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30 (2006) 700-708
21. He J.H., and Wu X.H. Variational iteration method: New development and applications. Comput. Math. Appl. 54 (2007) 881-894
22. He J.H. Variational approach for nonlinear oscillators. Chaos Solitons Fractals 34 (2007) 1430-1439
23. He J.H. Addendum: New interpretation of homotopy perturbation method. Int. J. Mod. Phys. B 20 (2006) 1141-1199
24. He J.H. Homotopy perturbation method: A new nonlinear analytical technique. J. Appl. Math. Comput. 135 (2000) 73-79
25. Ganji D.D., Afrouzi G.A., and Talarposhti R.A. Application of He's variational iteration method for solving the reaction-diffusion equation with ecological parameters. Comput. Math. Appl. 54 (2007) 1010-1017
26. Ganji D.D., Tari H., and Jooybari M.B. Variational iteration method and homotopy perturbation method for nonlinear evolution equations. Comput. Math. Appl. 54 (2007) 1018-1027
27. Ganji D.D., and Sadighi A. Exact solutions of nonlinear diffusion equations by variational iteration method. Comput. Math. Appl. 54 (2007) 1112-1121
28. Ganji D.D., and Sadighi A. Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods. Int. J. Nonlinear Sci. Numer. Simul. 8 (2007) 435-444
29. Gorji M., Ganji D.D., and Soleimani S. New application of He's homotopy perturbation method. Int. J. Nonlinear Sci. Numer. Simul. 8 (2007) 319-328
30. Ganji D.D., and Sadighi A. Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 411-418
31. Tari H., Ganji D.D., and Rostamian M. Approximate solutions of K (2, 2), KdV and Modified KdV equations by variational iteration method, homotopy perturbation method and homotopy analysis method. Int. J. Nonlinear Sci. Numer. Simul. 8 (2007) 203-210
32. Yusufoǧlu E. Homotopy perturbation method for solving a nonlinear system of second order boundary value problems. Int. J. Nonlinear Sci. Numer. Simul. 8 (2007) 353-358
33. Xu L. The variational iteration method for fourth order boundary value problems. Chaos Solitons Fractals (2007) 10.1016/j.chaos.2007.06.013
34. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 27-34
35. Biazar J., and Ghazvini H. He's variational iteration method for solving hyperbolic differential equations. Int. J. Nonlinear Sci. Numer. Simul. 8 (2007) 311-314
36. Xu L. Variational approach to solitons of nonlinear dispersive K (m, n) equations. Chaos Solitons Fractals 37 (2008) 137-143