Generalized approximation method and a thin film flow of a third grade fluid on a moving belt

被引:2
作者
Khan R.A. [1 ]
机构
[1] Centre for Advanced Mathematics and Physics, National University of Sciences and Technology(NUST), Campus of College of Electrical and Mechanical Engineering, Rawalpindi, Peshawar Road
关键词
Homotopy Analysis Method; Homotopy Perturbation Method; Grade Fluid; Shrinking Sheet; Thin Film Flow;
D O I
10.1007/s10598-010-9053-y
中图分类号
学科分类号
摘要
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. © 2010 Springer Science+Business Media, Inc.
引用
收藏
页码:41 / 50
页数:9
相关论文
共 17 条
  • [1] Ahmad B., Nieto J.J., Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions, Nonlinear Anal.
  • [2] van Dyke M., Perturbation Methods in Fluid Mechanics, (1975)
  • [3] Hayat T., Saif S., Abbas Z., The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet, Phys. Lett. A, 372, pp. 5037-5045, (2008)
  • [4] He J.H., Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178, 257, pp. 3-4, (1999)
  • [5] He J.H., A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int. J. Nonlinear Mech., 35, pp. 37-43, (2000)
  • [6] Keramati B., An approach to the solution of linear system of equations by He's homotopy perturbation method, Chaos, Solitons, Fractals
  • [7] Khan R.A., Rafique M., Existence and multiplicity results for some three-point boundary-value problems, Nonlinear Anal., 66, pp. 1686-1697, (2007)
  • [8] Khan R.A., Generalized approximations and rapid convergence of solutions of m-point boundary-value problems, Appl. Math. Comput., 188, pp. 1878-1890, (2007)
  • [9] Khan R.A., Generalized quasilinearization for periodic problems, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 14, pp. 497-507, (2007)
  • [10] Khan R.A., Generalized approximations method for heat radiation equations, Appl. Math. Comput.