On comparison of series and numerical solutions for second Painlevé equation

This attempt presents the series solution of second Painlevé equation by homotopy analysis method (HAM). Comparison of HAM solution is provided with that of the Adomian decomposition method (ADM), homotopy perturbation method (HPM), analytic continuation method, and Legendre Tau method. It is revealed that there is very good agreement between the analytic continuation and HAM solutions when compared with ADM, HPM, and Legendre Tau solutions. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010

[1]  E. L. Ince.  Ordinary differential equations , 1927 .

[2]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[3]  Shijun Liao,et al.  Comparison between the homotopy analysis method and homotopy perturbation method , 2005, Appl. Math. Comput..

[4]  S. Liao.  A new branch of solutions of boundary-layer flows over an impermeable stretched plate , 2005 .

[5]  S. Liao.  An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate , 2006 .

[6]  S. Abbasbandy.  THE APPLICATION OF HOMOTOPY ANALYSIS METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER , 2006 .

[7]  T. Hayat,et al.  Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt , 2007 .

[8]  S. Abbasbandy.  Soliton solutions for the Fitzhugh–Nagumo equation with the homotopy analysis method , 2008 .

[9]  T. Hayat,et al.  Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations , 2008 .

[10]  T. Hayat,et al.  Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet , 2008 .

[11]  Muhammad Awais,et al.  The influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method , 2008, Comput. Math. Appl..

[12]  Tasawar Hayat,et al.  The application of homotopy analysis method to thin film flows of a third order fluid , 2008 .

[13]  T. Hayat,et al.  Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface , 2008 .

[14]  Muhammad Awais,et al.  Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity , 2008 .

[15]  S. Abbasbandy.  Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method , 2008 .

[16]  S Nadeem,et al.  Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel's models of viscosities , 2009 .

[17]  Rahmat Ellahi,et al.  Effects of the slip boundary condition on non-Newtonian flows in a channel , 2009 .