Using a hybrid technique for the analytical solution of a coupled system of two-dimensional Burger’s equations,

Year 2018, Volume: 1 Issue: 3, 107 - 115, 14.11.2018

Kamal Shah , Atta Ullah

Abstract

Our aim in this paper is the analytical study of two dimensional non- linear system of Burger's equations. We present two problems for the efficiency of an hybrid techniques form by coupling Laplace transform with  Adomian polynomials method. The proposed method is named as Laplace transform Adomian decomposition method (LTADM). Two test examples are solved by the considered method to derive efficiency of the proposed method.

Keywords

Laplace Adomian decomposition method

References

• \bibitem{4} K. Shah, H. Khalil, R. A. Khan (2016) Analytical Solutions of Fractional Order Diffusion Equations by Natural Transform Method, \emph{Iran Journal of Science and Technology (Trans Sci:A)}, 1--12.
• \bibitem{1} Rogers, Colin, and William F. Shadwick. Bäcklund transformations and their applications. Academic press, 1982.
• \bibitem{a} Jafar Biazar and Hossein Aminikhah (2009) Study of convergence of homotopy perturbation mwthod for system of partial differential equations.
• \bibitem{c} Atta Ullah and Kamal Shah (2018) Numerical analysis of Lane Emden–Fowler equations. \emph{Journal of Taibah University for Science,} 1658--3655.
• \bibitem{d} N. S. Elgazery (2008) Numerical solution for the falkner-skan equations. \emph{Chaos, Solitons and Fractals,} 35 (\textbf{4}): 738--746.
• \bibitem{e} J. M. Burger (1948) A Mathematical model illustrating the theory of turbulence. \emph{Academic press, New York.}
• \bibitem{f} A. M. Yang Y. Z. Zhang and Y. Long (2013)Te Yang-Fourier transforms to heat-conduction in a semi-infnite fractal bar. \emph{Termal Science,} 37 (\textbf{3}): 707--713.
• \bibitem{g} Dehghan M, Manafian J and Saadatmandi A (2010) Solving nonlinear fractional partial differential equa- tions using the homotopy analysis method. \emph{Num. Meth. Partial Diff. Equns}, \textbf{26}(2): 448 --479.
• \bibitem{h}Y.Chen and H.L.An (2008), Numerical solutions of coupled Burgers equations with time-and spacefractional derivatives. \emph{Applied Mathematics and Computation,} \textbf{200}(1) : 87 -- 95.
• \bibitem{i} Y. Hu, Y. Luo and Z. Lu (2008) Analytical solution of the linear fractional differential equation by Adomian decomposition method. \emph{J.Comput.Appl.Math,} 215: 220--229.
• \bibitem{j} D.D Ganji, H Tari, M. Bakhshi Joobari (2007) Variational iteration method and homotopy perturbation method for nonlinear evolution equations. \emph{Int. J. Comput. Math. Appl,} 54: 1018--1027.
• \bibitem{k} H. Naher, F. A. Abdullah and M. A. Akbar (2011) The exp-function method for new exact solutions of the nonlinear partial differentialequations. \emph{International Journal of Physical Sciences,} (\textbf{29})6: 6706--6716.