Analytic solutions to diffusion equations

Mathematical and Computer Modelling

Volumn 51, Issue 5-6, 2010, Pages 649-657

  Paripour, M ^a   Babolian, E ^b   Saeidian, J ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b KHARAZMI UNIVERSITY   (Iran)

Author keywords

Analytic methods; Diffusion equation; Homotopy analysis method

Indexed keywords

ANALYTIC METHOD; ANALYTIC SOLUTION; AUXILIARY FUNCTIONS; CONVERGENCE REGION; DIFFUSION EQUATIONS; FUNCTIONAL EQUATION; HOMOTOPY ANALYSIS METHODS; INITIAL GUESS; WORKED EXAMPLES;

DIFFUSION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 74249119468     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2009.10.043     Document Type: Article

References (20)

1. Wu Z., Zhao J., Yin J., and Li H. Nonlinear Diffusion Equations (2001), World Scientific
2. S.J. Liao, Proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Dissertation, Shanghai Jiao Tong University, 1992
3. Liao S.J. Beyond Perturbation: An Introduction to Homotopy Analysis Method (2003), Chapman Hall/CRC Press, Boca Raton
4. Liao S.J. A kind of approximate solution technique which does not depend upon small parameters: A special example. Int. J. Non-Linear Mech. 30 (1995) 371-380
5. Liao S.J., and Chwang A.T. Application of homotopy analysis method in nonlinear oscillations. ASME. J. Appl. Mech. 65 (1998) 914-922
6. Liao S.J. An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude. Int. J. Non-Linear Mech. 38 (2003) 1173-1183
7. Liao S.J. On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. J. Fluid Mech. 488 (2003) 189-212
8. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147 (2004) 499-513
9. Liao S.J. Notes on the homotopy analysis method: Some definitions and theorems. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 983-997
10. Mollabahrami A., and Khani F. The homotopy analysis method to solve the Burgers-Huxley equation. Nonlinear Anal. RWA 10 (2009) 589-600
11. Abbasbandy S. The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Phys. Lett. A 361 (2007) 478-483
12. Abbasbandy S. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys. Lett. A 360 (2006) 109-113
13. Wazwaz A.M. Exact solutions to nonlinear diffusion equations obtained by the decomposition method. Appl. Math. Comput. 123 (2001) 109-122
14. Saeid E.A. The nonclassical solution of the inhomogeneous non-linear diffusion equation. Appl. Math. Comput. 98 (1999) 103-108
15. Dresner L. Similarity Solutions of Nonlinear Partial Differential Equations (1983), Pitman, New York
16. Changzheng Q. Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method. IMA J. Appl. Math. 62 (1999) 283-302
17. He J.H. Homotopy perturbation technique. Comp. Meth. Appl. Mech. Eng. 178 (1999) 257-262
18. Sajid M., Hayat T., and Asghar S. Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt. Nonlinear Dyn. 50 (2007) 27-35
19. Hayat T., and Sajid M. On analytic solution for thin film flow of a forth grade fluid down a vertical cylinder. Phys. Lett. A 361 (2007) 316-322
20. Sami Bataineh A., Noorani M.S.M., and Hashim I. The homotopy analysis method for Cauchy reaction-diffusion problems. Phys. Lett. A 372 (2008) 613-618