Application of Homotopy and Homotopy perturbation methods to differential equations of heat transfer and shear deformation of beams

Applied Mathematical Sciences

Volumn 5, Issue 21-24, 2011, Pages 1051-1063

  Manshadi, Mojtaba Dehghan ^a   Rohi, Ehsan ^a   Marzabadi, Faezeh Rasi ^a   Vaziry, M A ^b  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

^b AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Heat transfer; Homotopy; Homotopy perturbation; Shear deformation of beam

Indexed keywords

EID: 79959765666     PISSN: None     EISSN: 1312885X     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. A. Aziz, T.Y. Na, Perturbation Method in Heat Transfer, Hemisphere Publishing Corporation, Washington, (1984).
2. J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng. 167 (1998) 57-68.
3. J.H. He, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Comput. Methods Appl. Mech. Eng. 167 (1998) 69-73.
4. J.H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Internat. J. Non-linear Mech. 34 (1999) 699-708.
5. J.H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114 (2000) 115-123.
6. J.H. He, X.H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons Fractals 29 (2006) 108-113.
7. S. Abbasbandy, S. Liao. A new modification of false position method based on homotopy analysis method, Appl.Math.& Mech. 2008, 29(2) 223-228
8. A. Rezania; A. Ghorbali; G. Domairry; H. Bararnia. Consideration of transient heat conduction in a semi-infinite medium using homotopy analysis method, Appl.Math.& Mech. 2008, 29(12) 1625-1632
9. Jing ZHU, Lian-Cun ZHENG, Xin-Xin ZHANG. Analytical solution to stagnation-point flow and heat transfer over a stretching sheet based on homotopy analysis, Appl.Math. Mech. -Engl. Ed. 2009, 30(4) 463-474
10. J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng. 178 (1999) 257-262.
11. J.H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Internat. J. Non-linear Mech. 35 (2000) 37-43.
12. J.H. He, Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput. 135 (2003) 73-79.
13. J.H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput. 151 (2004) 287-92.
14. J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons Fractals 26 (2005) 695-700.
15. J.H. He, Homotopy perturbation method for bifurcation of nonlinear problems, Internat. J. Nonlinear Sci. Numer. Simul. 6 (2005) 07-208.
16. E.M. Abulwafa, M.A. Abdou,AA. Mahmoud, The solution of nonlinear coagulation problem with mass loss, Chaos, Solitons Fractals 29 (2006) 313-330.
17. A.A. Soliman,A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations, Chaos, Solitons Fractals 29 (2006) 294-302.
18. S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems. Ph.D. Thesis, Shanghai Jiao Tong University, (1992).
19. D.D. Ganji, A. Sadighi, Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, Journal of Computational and Applied Mathematics 207 (2007) 24.