Analysis of Adomian decomposition applied to a third-order ordinary differential equation from thin film flow

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 10, 2007, Pages 2315-2324

  Momoniat, E ^a   Selway, T A ^a   Jina, K ^a  

^a UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

Adomian decomposition; Thin film; Third order ode

Indexed keywords

APPROXIMATION THEORY; CONTACT ANGLE; CONVERGENCE OF NUMERICAL METHODS; THIN FILMS;

ADOMIAN DECOMPOSITION; THIRD-ORDER ODE;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 33847160298     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.03.021     Document Type: Article

References (19)

1. Abbaoui K., and Cherruauly Y. Convergence of Adomian's method applied to differential equations. Math. Comput. Modelling 28 (1994) 103-109
2. Himoun N., Abbaoui K., and Cherruauly Y. New results of convergence of Adomian's method. Kybernetes 28 (1999) 423-429
3. Bernis F., and Peletier L.A. Two problems from draining flows involving third-order ordinary differential equations. SIAM J. Math. Anal. 27 (1996) 515-527
4. Biazar J., Babolian E., and Islam R. Solution of the system of ordinary differential equations by Adomian decomposition method. Appl. Math. Comput. 147 (2004) 713-719
5. Casasús L., and Al-Hayani W. The decomposition method for ordinary differential equations with discontinuities. Appl. Math. Comput. 131 (2002) 245-251
6. Duffy B.R., and Wilson S.K. A third-order differential equation arising in thin-film flows and relevant to Tanner's Law. Appl. Math. Lett. 10 (1997) 63-68
7. Ford W.F. A third-order differential equation. SIAM Rev. 34 (1992) 121-122
8. Greenspan H.P. On the motion of a small viscous droplet that wets a surface. J. Fluid Mech. 84 (1978) 125-143
9. Hocking L.M. The spreading of a thin drop by gravity and capillarity. Q. J. Mech. Appl. Math. 36 (1983) 55-69
10. King J.R., and Bowen M. Moving boundary problems and non-uniqueness for the thin film equation. Euro. J. Appl. Math. 12 (2001) 321-356
11. Mahmood A.S., Casasús L., and Al-Hayani W. The decomposition method for stiff systems or ordinary differential equations. Appl. Math. Comput. 167 (2005) 964-975. doi:10.1016/j.amc.2004.06.134
12. Middleman S. Modelling Axisymmetric Flows (1995), Academic Press, New York
13. Moriarty J.A., and Schwartz L.W. Effective slip in numerical calculations of moving-contact-line problems. J. Engrg. Math. 26 (1992) 81-86
14. Myers T.G. Thin films with high surface tension. SIAM Rev. 40 (1998) 441-462
15. Polyanin A.D., and Zaitsev V.F. Handbook of Exact Solutions for Ordinary Differential Equations (1995), CRC Press Inc., Boca Raton, Florida
16. Smyth N.F., and Hill J.M. High-order nonlinear diffusion. IMA J. Appl. Math. 40 (1988) 73-86
17. Tanner L.H. The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12 (1979) 1473-1484
18. Tuck E.O., and Schwartz L.W. Numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows. SIAM Rev. 32 (1990) 453-469
19. Troy W.C. Solutions of third-order differential equations relevant to draining and coating flows. SIAM J. Math. Anal. 24 (1993) 155-171