Generalized approximation method and a thin film flow of a third grade fluid on a moving belt
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We develop a generalized approximation method (GAM) to obtain a solution of a thin film flow of a third grade fluid on a moving belt. The GAM generates a monotone sequence of solutions of linear problems. The sequence of solutions of linear problems converges monotonically and rapidly to a solution of the original nonlinear problem. We present some numerical simulations to illustrate and confirm our results.
KeywordsHomotopy Analysis Method Homotopy Perturbation Method Grade Fluid Shrinking Sheet Thin Film Flow
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- 1.B. Ahmad and J. J. Nieto, “Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions,” Nonlinear Anal. (TMA), doi: 10.1016/j.na.2007.09.018.
- 4.J. H. He, “Homotopy perturbation technique,” Comput. Methods Appl. Mech. Eng., 178 (257), 3 – 4 (1999).Google Scholar
- 6.B. Keramati, “An approach to the solution of linear system of equations by He’s homotopy perturbation method,” Chaos, Solitons, Fractals, doi: 10.1016/j.chaos.2007.11.020.
- 10.R. A. Khan, “Generalized approximations method for heat radiation equations,” Appl. Math. Comput., Doi: 10.1016/j.amc.2009.02.028.
- 11.R. A. Khan, “The generalized approximations and nonlinear heat transfer equations,” Elec. J. Qual. Theory Differ. Eq., 2, 1–15 (2009).Google Scholar
- 16.A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Thin film flow of a third grade fluid on a moving belt by He’s homotopy perturbation method,” Int J. Non-Linear Sci. Numer. Simul., 7, 1 – 8 (2006).Google Scholar
- 17.A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane,” Chaos, Solitons, Fractals, doi: 10.1016/j.chaos.2006.05.026.