ADM-Padé solutions for generalized Burgers and Burgers-Huxley systems with two coupled equations

We present an approximate numerical solution to generalized Burgers and Burgers-Huxley systems with two coupled equations using the ADM-Pade technique which is a combination of the Adomian decomposition method and Pade approximation. The Pade technique is used to enhance the accuracy and speed up the convergence rate of the truncated series solution produced by the ADM. Results are given in graphical form for explicit examples of the two systems.

[1]  Lokenath Debnath,et al.  Linear Partial Differential Equations , 2012 .

[2]  Tamer A. Abassy,et al.  The solution of Burgers’ and good Boussinesq equations using ADM–Padé technique , 2007 .

[3]  L. Debnath Nonlinear Partial Differential Equations for Scientists and Engineers , 1997 .

[4]  A. Alharbi,et al.  APPROXIMATE SOLUTION FOR TIME-DELAYED CONVECTIVE FISHER EQUATION BY ADM-PADÉ TECHNIQUE , 2010 .

[5]  I. Bajunaid,et al.  APPROXIMATE SOLUTION FOR THE GENERALIZED TIME-DELAYED BURGERS-HUXLEY EQUATION , 2007 .

[6]  Y. Cherruault Convergence of Adomian's method , 1990 .

[7]  A. A. Soliman,et al.  The decomposition method for solving the coupled modified KdV equations , 2008, Math. Comput. Model..

[8]  E. S. Ismail,et al.  Accuracy of the Adomian decomposition method applied to the Lorenz system , 2006 .

[9]  I. Hashim,et al.  Non-perturbative solution of free-convective boundary-layer equation by Adomian decomposition method , 2007 .

[10]  Yves Cherruault,et al.  Convergence of Adomian's Method and Applications to Non‐linear Partial Differential Equations , 1992 .

[11]  Mohd. Salmi Md. Noorani,et al.  Further accuracy tests on Adomian decomposition method for chaotic systems , 2008 .

[12]  S. Motamen,et al.  Nonlinear diffusion equation , 2002 .

[13]  I. Hashim,et al.  Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field , 2008 .

[14]  Dogan Kaya,et al.  Exact and numerical solutions of generalized Drinfeld-Sokolov equations , 2008 .

[15]  Yoshikazu Giga,et al.  Nonlinear Partial Differential Equations , 2004 .

[16]  K. R. Raslan,et al.  On the exact and numerical solution of the time-delayed Burgers equation , 2008, Int. J. Comput. Math..

[17]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[18]  Viriato Semiao,et al.  Numerical study of modified Adomian's method applied to Burgers equation , 2007 .

[19]  Abdul-Majid Wazwaz,et al.  Analytical approximations and Padé approximants for Volterra's population model , 1999, Appl. Math. Comput..

[20]  Mohd. Salmi Md. Noorani,et al.  Comparing numerical methods for the solutions of the Chen system , 2007 .

[21]  Esmail Babolian,et al.  New method for calculating Adomian polynomials , 2004, Appl. Math. Comput..