Abstract
The aspire of this article is to bring in a new approximate method, that is to say the Laplace Padé decomposition method which is a mixture of Laplace decomposition and Padé approximation to offer an analytical approximate way out to magnetohydrodynamics flow over a nonlinear porous stretching sheet. This new iteration approach provides us with a convenient way to approximate solution. A closed agreement between the obtained solution and some well-known results has been established. The proposed procedure can be applied to handle other nonlinear problems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Adomian G.: The Decomposition Method. Kluwer, Boston (1994)
Baker G.A.: Essentials of Padé Approximants. Academic Press, London (1975)
Chun C., Jafari H., Kim Y.: Numerical method for the wave and nonlinear diffusion equations with the homotopy perturbation method. Comput. Math. Appl. 57, 1226–1231 (2009)
Chaim T.C.: Hydromagnetic flow over a surface stretching with a power law velocity. Int. J. Eng. Sci. 33, 429–435 (1995)
Ghotbi A.R.: Homotopy analysis method for solving the MHD flow over a non-linear stretching sheet. Commun. Nonlinear Sci. Numer. Simul. 14, 2653–2663 (2009)
Hosseini M.M.: Adomian decomposition method with Chebyshev polynomials. Appl. Math. Comput. 175, 1685–1693 (2006)
Hosseini M.M.: Numerical solution of ordinary differential equations with impulse solution. Appl. Math. Comput. 163, 373–381 (2005)
Hosseini M.M.: Adomian decomposition method for solution of differential-algebraic equations. J. Comput. Appl. Math. 197, 373–381 (2006)
Hosseini M.M.: Adomian decomposition method for solution of nonlinear differential algebraic equations. Appl. Math. Comput. 181, 1737–1744 (2006)
Hussain M., Khan M.: Modified Laplace decomposition method. Appl. Math. Sci. 4, 1769–1783 (2010)
Jafari H., Zabihi M., Saidy M.: Application of homotopy-perturbation method for solving gas dynamics equation. Appl. Math. Sci. 2, 2393–2396 (2008)
Jafari H., Momani S.: Solving fractional diffusion and wave equations by modified homotopy perturbation method. Phys. Lett. A. 370, 388–396 (2007)
Jafari H., Sadeghi J., Zabihi M., Amani A. R.: Application of homotopy perturbation method for two coupled scalar fields. J. Comput. Math. 1, 56–66 (2008)
Jafari H., Golbabai A., Seifi S., Sayevand K.: Homotopy analysis method for solving multi-term linear and nonlinear diffusion wave equations of fractional order. Comput. Math. Appl. 59, 1337–1344 (2010)
Jafari H., Saeidy M., Vahidi J.: The homotopy analysis method for solving fuzzy system of linear equations. Int. J. Fuzzy Syst. 11, 308–313 (2009)
Jafari H., Firozjaee M.A.: Application of homotopy analysis method for nonlinear Sturm-Liouville problems. J. Adv. Res. Differ. Equ. 1, 11–20 (2009)
Khuri S.A.: A Laplace decomposition algorithm applied to class of nonlinear differential equations. J. Appl. Math. 4, 141–155 (2001)
Khan M., Hussain M.: Application of Laplace decomposition method on semi infinite domain. Numer. Algorithms 56, 211–218 (2011)
Khan M., Gondal M.A.: New modified Laplace decomposition algorithm for Blasius flow equation. J. Adv. Res. Sci. Comput. 2, 35–43 (2010)
Khan M., Gondal M.A.: A new analytical solution of foam drainage equation by Laplace decomposition method. J. Adv. Res. Differ. Equ. 2, 53–64 (2010)
Khan M., Gondal M.A.: Application of Laplace decomposition method to solve systems of nonlinear coupled partial differential equations. J. Adv. Res. Sci. Comput. 2, 1–14 (2010)
Nadeem S., Hussain A., Khan M.: HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. Commun. Nonlinear Sci. Numer. Simul. 15, 475–481 (2010)
Nadeem S., Hussain A., Khan M.: Stagnation flow of a Jeffrey fluid over a shrinking sheet. Zeit. fur. Nat. A. 65a, 1–9 (2010)
Pavlov K.B.: Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a surface. Magni. Gidrodi. 4, 146–147 (1995)
Yildirim A., Öziş T.: Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method. Phys. Lett. A. 369, 70–76 (2007)
Yildirim A., Öziş T.: Solutions of singular IVPs of Lane-Emden type by the variational iteration method. Nonlinear Anal. Theor. Methods Appl. 70, 2480–2484 (2009)
Yildirim: Application of He’s variational iteration method to nonlinear integro-differential equations. Zeit. fur. Nat. A. 63a, 418–422 (2008)
Yildirim A., Sefa S.A.: Analytical solution of linear and non-linear space-time fractional reaction-diffusion equations. Int. J. Chem. Real. Eng. 8, A110S (2010)
Yildirim A.: Exact solutions of poisson equation for electrostatic potential problems by means of the variational iteration method. Int. J. Nonlinear Sci. Numer. Simul. 10, 867–871 (2009)
Yildirim A.: Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations. Int. J. Numer. Methods Biomed. Eng. 10, 266–272 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gondal, M.A., Khan, M. & Omrani, K. A New Analytical Approach to Solve Magnetohydrodynamics Flow Over a Nonlinear Porous Stretching Sheet by Laplace Padé Decomposition Method. Results. Math. 63, 289–301 (2013). https://doi.org/10.1007/s00025-011-0198-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-011-0198-6