Application of homotopy perturbation method in nonlinear heat diffusion-convection-reaction equations

Open Mechanics Journal

Volumn 1, Issue 1, 2007, Pages 20-25

  Tolou, N ^a   Ganji, D D ^a   Hosseini, M J ^a   Ganji, Z Z ^a  

^a UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

Black scholes equation; Fokker planck equation; Homotopy perturbation method; Nonlinear diffusion convection reaction equations (DCRE); Nonlinear PDE

Indexed keywords

EID: 41149140086     PISSN: None     EISSN: 18741584     Source Type: Journal    
DOI: 10.2174/1874158400701010020     Document Type: Article

References (33)

1. Bellman R. Perturbation Techniques in Mathematic, Physics and Engineering, Holt, Rinehart & Winston, New York, 1964.
2. Cole JD. Perturbation Methods in Applied Mathematics, Blaisedell, Waltham, MA, 1968.
3. Omalley RE Jr. Introduction to Singular perturbation, Academic, New York, 1974.
4. Nayfeh AH. Perturbation Methods, Wiley, New York, 1973.
5. Van Dyke M. Perturbation Methods in Fluid Mechanics, Annotated Edition, parabolic press, Stanford, CA, 1975.
6. Liu GL. New research directions in singular perturbation theory: artificial parameter approach and inverse-perturbation technique, Conference of 7th Modern Mathematics and Mechanics, Shanghai, 1997.
7. Ganji DD, Jamshidi N. Application of He's Homotopy-perturbation Method to Nonlinear Coupled Systems of Reaction-diffusion Equations. International Journal of Nonlinear Science and Numerical Simulation 2006; 7: 413-420.
8. Ganji DD, Hashemi SH. Exact solutions of Laplace equation by homotopy-perturbation and Adomian decomposition methods, Phys Lett A 2007; 367: 83-87.
9. He JH. approximate analytical solution for seepage flow with fractional derivatives in porous media. J Comput Math Appl Mech Eng 1998; 167: 57-68.
10. He JH. Approximate solution for nonlinear differential equations with convolution product nonlinearities. Comput Math Appl Mech Eng 1998; 167: 69-73.
11. He JH. variational iteration method: a kind of nonlinear analytical technique: some examples. Int J Non-Linear Mexh 1999; 344: 699.
12. Tari H, Ganji DD. Approximate explicit solutions of nonlinear BBMB equations by He's methods and comparison with the exact solution. Phys Lett 2007; 367: 95-101.
13. Rafei M, Ganji DD. Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method. International Journal of Nonlinear Sciences and Numerical Simulation 2006; 7(3): 321-328.
14. Tari H, Ganji DD, Rostamian M. Approximate solutions of K (2,2), KdV and modified KdV equations by variational iteration method, homotopy perturbation method and homotopy analysis method. International Journal of Nonlinear Sciences and Numerical Simulation 2007; 8(2): 303-310.
15. Cveticanin L. Homotopy - perturbation method for pure nonlinear differential equation, Chaos Solitins Fractals, 2005, in press.
16. He JH. Chaos: Limit cycle and bifurcation of nonlinear problems. Chaos Solitons Fractals 2005; 26: 827.
17. He JH. Periodic solutions and bifurcations of delay-differential equations. Phys Lett A 2005; 347: 228-230.
18. He JH. Homotopy perturbation method for solving boundary value problems. Phys Lett A 2006; 350: 87-88.
19. El-Wakil SA, Abulwafa EM, Abdou MA, Elhanbaly A. Maximum-entropy approach with higher moments for solving Fokker- Planck equation. Physica A 2002; 315: 480-492.
20. Wie GW. A unified approach for the solution of the Fokker-Planck equation. J Phys A Math Gen 2000; 33: 4935-4953.
21. Black F, Sholes M. The pricing of options and corporate liabilities. J Polit Econ 1973; 81: 637-659.
22. Kwok YK. Mathematical Models of Financial Derivatives, Springer, Berlin. 1998.
23. Spichak S, Stongnij V. Symmetry classification and exact solutions of the one-dimensional Fokker-Planck equation with arbitrary coefficients of drift and diffusion. J Phys A Math Gen 1999; 32: 8341-8353.
24. Lieberman MA, Lichtenberg AJ. Principles of Plasma Discharges and Materials Processing (Wiley, New York, 1994).
25. El-Wakil SA, Zahran MA, Abdou MA. The operator method for solving the Fractional Fokker-Planck Equation. JQSRT 2003; 317: 327.
26. He JH. Homotopy perturbation technique. J Comput Methods Appl Mech Eng 1999; 178: 257-262.
27. He JH. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int J Non-Linear Mech 2000; 35: 37-43.
28. He JH. Homotopy perturbation method: a new nonlinear analytical technique. J Appl Math Comp 2000; 135: 73-79.
29. He JH. The homotopy perturbation method for nonlinear oscillators with discontinuities. J Appl Math Comput 2004; 151: 287-292.
30. Ganji DD, Sadighi A. Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, J Comput Appl Math 2007; 207: 24-34.
31. Hassan Khaleghi, Ganji DD, Sadighi A. Application of variational iteration and homotopy-perturbation methods to nonlinear heat transfer equations with variable coefficients. Numerical Heat Transfer. Part A 2007; 52: 25-42.
32. Rajabi A, Ganji DD, Taherian H. Application of homotopyperturbation method to nonlinear heat conduction and convection equations. Phys Lett A 2007; 360: 570-573.
33. Ganji DD. The application of He's homotopy-perturbation method to nonlinear equations arising in heat transfer. Phys Lett A 2006; 355: 337-341.