# zbMATH — the first resource for mathematics

Analysis of Adomian decomposition applied to a third-order ordinary differential equation from thin film flow. (English) Zbl 1127.34302
The authors use the Adomian decomposition method to determine a power series approximation of the solution of the equation
$y'''=y^{-k}$ with a constant $$k.$$ It is shown that the domain of convergence depends on $$k.$$ It is also plotted how the contact angle increases with increasing value of $$k.$$

##### MSC:
 34A45 Theoretical approximation of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems, general theory 34C60 Qualitative investigation and simulation of ordinary differential equation models
Full Text:
##### References:
 [1] Abbaoui, K.; Cherruauly, Y., Convergence of adomian’s method applied to differential equations, Math. comput. modelling, 28, 103-109, (1994) · Zbl 0809.65073 [2] Himoun, N.; Abbaoui, K.; Cherruauly, Y., New results of convergence of adomian’s method, Kybernetes, 28, 423-429, (1999) · Zbl 0938.93019 [3] Bernis, F.; Peletier, L.A., Two problems from draining flows involving third-order ordinary differential equations, SIAM J. math. anal., 27, 515-527, (1996) · Zbl 0845.34033 [4] Biazar, J.; Babolian, E.; Islam, R., Solution of the system of ordinary differential equations by Adomian decomposition method, Appl. math. comput., 147, 713-719, (2004) · Zbl 1034.65053 [5] Casasús, L.; Al-Hayani, W., The decomposition method for ordinary differential equations with discontinuities, Appl. math. comput., 131, 245-251, (2002) · Zbl 1030.34012 [6] Duffy, B.R.; Wilson, S.K., A third-order differential equation arising in thin-film flows and relevant to tanner’s law, Appl. math. lett., 10, 63-68, (1997) · Zbl 0882.34001 [7] Ford, W.F., A third-order differential equation, SIAM rev., 34, 121-122, (1992) [8] Greenspan, H.P., On the motion of a small viscous droplet that wets a surface, J. fluid mech., 84, 125-143, (1978) · Zbl 0373.76040 [9] Hocking, L.M., The spreading of a thin drop by gravity and capillarity, Q. J. mech. appl. math., 36, 55-69, (1983) · Zbl 0507.76100 [10] King, J.R.; Bowen, M., Moving boundary problems and non-uniqueness for the thin film equation, Euro. J. appl. math., 12, 321-356, (2001) · Zbl 0985.35113 [11] Mahmood, A.S.; Casasús, L.; Al-Hayani, W., The decomposition method for stiff systems or ordinary differential equations, Appl. math. comput., 167, 964-975, (2005) · Zbl 1082.65561 [12] Middleman, S., Modelling axisymmetric flows, (1995), Academic Press New York [13] Moriarty, J.A.; Schwartz, L.W., Effective slip in numerical calculations of moving-contact-line problems, J. engrg. math., 26, 81-86, (1992) [14] Myers, T.G., Thin films with high surface tension, SIAM rev., 40, 441-462, (1998) · Zbl 0908.35057 [15] Polyanin, A.D.; Zaitsev, V.F., Handbook of exact solutions for ordinary differential equations, (1995), CRC Press Inc. Boca Raton, Florida · Zbl 0855.34001 [16] Smyth, N.F.; Hill, J.M., High-order nonlinear diffusion, IMA J. appl. math., 40, 73-86, (1988) · Zbl 0694.35091 [17] Tanner, L.H., The spreading of silicone oil drops on horizontal surfaces, J. phys. D: appl. phys., 12, 1473-1484, (1979) [18] Tuck, E.O.; Schwartz, L.W., Numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows, SIAM rev., 32, 453-469, (1990) · Zbl 0705.76062 [19] Troy, W.C., Solutions of third-order differential equations relevant to draining and coating flows, SIAM J. math. anal., 24, 155-171, (1993) · Zbl 0807.34030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.