Variational iteration method for unsteady flow of gas through a porous medium using He's polynomials and Pade approximants

Computers and Mathematics with Applications

Volumn 58, Issue 11-12, 2009, Pages 2182-2189

  Noor, Muhammad Aslam ^a   Mohyud Din, Syed Tauseef ^a  

^a COMSATS Institute of Information Technology ^*  (Pakistan)

Author keywords

He's polynomials; Nonlinear problems; Pade approximants; Porous medium; Unsteady flow of gas; Variational iteration method

Indexed keywords

HE'S POLYNOMIALS; NONLINEAR PROBLEMS; PADE APPROXIMANTS; POROUS MEDIUM; VARIATIONAL ITERATION METHOD;

AERODYNAMICS; ALGORITHMS; FLOW OF GASES; FLUID DYNAMICS; HELIUM; LINEARIZATION; OSCILLATORS (MECHANICAL); PERTURBATION TECHNIQUES; POLYNOMIALS; POROUS MATERIALS; UNSTEADY FLOW;

ITERATIVE METHODS;

EID: 68049116320     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.03.016     Document Type: Article

References (49)

1. H. Carslaw, J. Jaeger, Conduction of heat in solids, Oxford, London, 1947
2. Davis H.T. Introduction to Nonlinear Differential and Integral Equations (1962), Dover Publications, New York
3. Kidder R.E. Unsteady flow of gas through a semi-infinite porous medium. J. Appl. Mech. 27 (1957) 329-332
4. Muskat M. Flow of homogeneous fluids. J. Ed. Ann. Arb. M1 (1946)
5. R.C. Roberts, Unsteady flow of gas through a porous medium, in: Proceedings of the First US National Congress of Applied Mechanics, Ann Arbor, MI, 1952, pp. 773-776
6. Wazwaz A.M. The modified decomposition method applied to unsteady flow of gas through a porous medium. Appl. Math. Comput. 118 (2001) 123-132
7. Boyd J.P. Pade approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain. Comput. Phys. 11 3 (1997) 299-303
8. He J.H. Some asymptotic methods for strongly nonlinear equation. Int. J. Nod. Phys. 20 20 (10) (2006) 1144-1199
9. He J.H. Variational iteration method, A kind of nonlinear analytical technique, some examples. Internat. J. Non-linear Mech. 34 4 (1999) 699-708
10. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 2-3 (2000) 115-123
11. He J.H., and Wu X.H. Construction of solitary solution and compaction-like solution by variational iteration method. Chaos Solitons Fractals 29 1 (2006) 108-113
12. He J.H. Variational iteration method- Some recent results and new interpretations. J. Comput. Appl. Math. 207 (2007) 3-17
13. He J.H., and Wu X.H. Variational iteration method: New development and applications. Comput. Math. Appl. 54 (2007) 881-894
14. He J.H. The variational iteration method for eighth-order initial boundary value problems. Phys. Scripta 76 6 (2007) 680-682
15. He J.H. Homotopy perturbation technique. Comput. Math. Appl. Mech, Eng. (1999) 178-257
16. He J.H. Homotopy perturbation method for solving boundary value problems. Phys. Lett. A 350 (2006) 87-88
17. He J.H. Comparison of homotopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156 (2004) 527-539
18. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simul. 6 2 (2005) 207-208
19. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl. Math. Comput. 151 (2004) 287-292
20. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Non-linear Mech. 35 1 (2000) 115-123
21. Inokuti, Sekine H., and Mura T. General use of the Lagrange multiplier in nonlinear mathematical physics. In: Nemat-Naseer S. (Ed). Variational Method in the Mechanics of Solids (1978), Pergamon press, New York 156-162
22. Abbasbandy S. A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials. J. Comput. Appl. Math. 207 (2007) 59-63
23. Abbasbandy S. Numerical solutions of nonlinear Klein-Gordon equation by variational iteration method. Internat. J. Numer. Methods Eng. 70 (2007) 876-881
24. Abbasbandy S. Numerical methods for non-linear wave and diffusion equation by the variational iteration method. Internat. J. Numer. Methods Eng. (2008)
25. Biazar J., and Ghazvini H. He's variational iteration method for fourth-order parabolic equations. Comput. Math. Appl. 54 (2007) 1047-1054
26. Ganji D.D., and Golbabai A. Application of He's variational iteration method for solving the reaction-diffusion equation with ecological parameters. Comput. Math. Appl. 54 (2007) 1010-1017
27. Ghorbani A., and Nadjfi J.S. He's homotopy perturbation method for calculating Adomian's polynomials. Int. J. Nonlinear Sci. Numer. Simul. 8 2 (2007) 229-332
28. Ghorbani A. Beyond Adomian polynomials: He polynomials. Chaos Solitons Fractals (2007) 10.1016/j.chaos.2007.06.034
29. Momani S., and Odibat Z. Application of He's variational iteration method to Helmholtz equations. Chaos Solitons Fractals 27 5 (2006) 1119-1123
30. Marnica V., and Herisanu N. Periodic solutions for some nonlinear oscillators by He's variational iteration method. Comput. Math. Appl. 54 (2007) 1188-1196
31. S.T. Mohyud-Din, A reliable algorithm for Blasius equation, in: Proceedings of International Conference on Mathematical Sciences, Selangor, Malaysia, 2007, pp. 616-626
32. Mohyud-Din S.T., and Noor M.A. Homotopy perturbation method for solving fourth order boundary value problems. Math. Prob. Eng. (2006) 1-15
33. Noor M.A., and Mohyud-Din S.T. An efficient algorithm for solving fifth order boundary value problems. Math. Comput. Modelling. 45 (2007) 954-964
34. Noor M.A., and Mohyud-Din S.T. Homotopy perturbation method for solving sixth-order boundary value problems. Math. Comput. Appl. (2007)
35. Noor M.A., and Mohyud-Din S.T. Homotopy method for solving eighth order boundary value problem. J. Math. Anal. Appl. Th. 1 2 (2006) 161-169
36. Noor M.A., and Mohyud-Din S.T. Approximate solutions of Flieral Petviashivili equation and its variants. Int. J. Math. Comput. Sci. 2 4 (2007) 345-360
37. Noor M.A., and Mohyud-Din S.T. A reliable approach for solving linear and nonlinear sixth-order boundary value problems. Int. J. Comput. Appl. Math. (2007)
38. Noor M.A., and Mohyud-Din S.T. An efficient method for fourth order boundary value problems. Comput. Math. Appl. 54 (2007) 1101-1111
39. Noor M.A., and Mohyud-Din S.T. Variational iteration technique for solving higher order boundary value problems. Appl. Math. Comput. 189 (2007) 1929-1942
40. Noor M.A., and Mohyud-Din S.T. Variational iteration technique for solving tenth-order boundary value problems. A. J. Math. Math. Sci. (2007)
41. Noor M.A., and Mohyud-Din S.T. Variational iteration decomposition method for solving eighth-order boundary value problems. Diff. Eqns. Nonlin. Mech. (2007) 10.1155/2007/19529
42. Noor M.A., and Mohyud-Din S.T. Variational decomposition method for solving singular initial value problems. Int. J. Pure Appl. Math. (2007)
43. Noor M.A., and Mohyud-Din S.T. Variational iteration method for solving higher-order nonlinear boundary value problems using He's polynomials. Int. J. Nonlinear Sci. Numer. Simul. 9 2 (2008)
44. Wazwaz A.M. The variational iteration method for solving linear and nonlinear system of PDES. Comput. Math. Appl. 54 (2007) 895-902
45. Xu L. He's homotopy perturbation method for a boundary layer equation in unbounded domain. Comput. Math. Appl. 54 (2007) 1067-1070
46. Xu L. Variational iteration method for solving integral equations. Comput. Math. Appl. 54 (2007) 1071-1078
47. Baker G.A. Essentials of Pade Approximants (1975), Academic press, London
48. S. Momani, V.S. Erturk, Solution of nonlinear oscillators by modified differential transform method, Comput. Math. Appl. (2007), in press (doi:10.1016/j.camwa.2007.05.009)
49. Wazwaz A.M. The modified decomposition method and Pade approximants for solving Thomas-Fermi equation. Appl. Math. Comput. 105 (1999) 11-19