Analytical Solutions of the Slip Magnetohydrodynamic Viscous Flow over a Stretching Sheet by Using the Laplace–Adomian Decomposition Method

2012 ◽  
Vol 67 (5) ◽  
pp. 248-254 ◽  
Author(s):  
Hadi Roohani Ghehsareh ◽  
Saeid Abbasbandy ◽  
Babak Soltanalizadeh
Keyword(s):  
Decomposition Method ◽  
Stretching Sheet ◽  
Adomian Decomposition Method ◽  
Mhd Flow ◽  
Similarity Solutions ◽  
Model Parameters ◽  
Series Solutions ◽  
Stretching Surface ◽  
Convergence Domain ◽  
Adomian Decomposition

In this research, the Laplace-Adomian decomposition method (LADM) is applied for the analytical and numerical treatment of the nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow under slip condition over a permeable stretching surface. The technique is well applied to approximate the similarity solutions of the problem for some typical values of model parameters. The obtained series solutions by the LADM are combined with the Pad´e approximation to improve the accuracy and enlarge the convergence domain of the obtained results. Through tables and figures, the efficiency of the presented method is illustrated.

On the Analytic Solution for a Steady Magnetohydrodynamic Equation

2013 ◽  
Vol 68 (6-7) ◽  
pp. 412-420 ◽  
Author(s):  
Babak Soltanalizadeh ◽  
Hadi Roohani Ghehsareh ◽  
Ahmet Yıldırım ◽  
Saeid Abbasbandy
Keyword(s):  
Analytic Solution ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Mhd Flow ◽  
Similarity Solutions ◽  
Model Parameters ◽  
Series Solutions ◽  
Magnetohydrodynamic Equation ◽  
Adomian Decomposition ◽  
Axisymmetric Bodies

The purpose of this study is to apply the Laplace-Adomian Decomposition Method (LADM) for obtaining the analytical and numerical solutions of a nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. By using this method, the similarity solutions of the problem are obtained for some typical values of the model parameters. For getting computational solutions, we combined the obtained series solutions by LADM with the Padé approximation. The method is easy to apply and gives high accurate results. The presented results through tables and figures show the efficiency and accuracy of the proposed technique.

scholarly journals Solving Fractional-Order Logistic Equation Using a New Iterative Method

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Sachin Bhalekar ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Iterative Method ◽  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Logistic Equation ◽  
Series Solutions ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
New Iterative Method

A fractional version of logistic equation is solved using new iterative method proposed by Daftardar-Gejji and Jafari (2006). Convergence of the series solutions obtained is discussed. The solutions obtained are compared with Adomian decomposition method and homotopy perturbation method.

THE NEW ADM–PADÉ TECHNIQUE FOR THE GENERALIZED EMDEN–FOWLER EQUATIONS

2010 ◽  
Vol 24 (12) ◽  
pp. 1237-1254 ◽  
Author(s):  
HONGMEI CHU ◽  
YINPING LIU
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Padé Approximant ◽  
Convergence Domain ◽  
Adomian Polynomials ◽  
Solution Series ◽  
Pade Approximant ◽  
Adomian Decomposition ◽  
New Type

In this paper, the Emden–Fowler equations are investigated by employing the Adomian decomposition method (ADM) and the Padé approximant. By using the new type of Adomian polynomials proposed by Randolph C. Rach in 2008, our obtained solution series converges much faster than the regular ADM solution of the same order. Meanwhile, we note that the solutions obtained by using the new ADM–Padé technique have much higher accuracy and larger convergence domain than those obtained by using the regular ADM together with the Padé technique. Finally, comparison of our new obtained solutions are given with those existing exact ones graphically to illustrate the validity and the promising potential of the new ADM–Padé technique for solving nonlinear problems.

Series Solutions for South African Banks Users Using the Adomian Decomposition Method

2020 ◽  
Vol 17 (7) ◽  
pp. 2940-2946
Author(s):  
M. C. Kekana ◽  
T. O. Tong ◽  
M. Y. Shatalov ◽  
S. P. Moshokoa
Keyword(s):  
South African ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
National Standard ◽  
Series Solutions ◽  
Personal Interaction ◽  
Adomian Decomposition

In this paper, A model for the four major South African banks namely Absa, First national, Standard and Nedbank users is developed and investigated. Series solutions for South African banks users is obtained using the Adomian decomposition method under factors emigration, immigration, advertisement of each bank and personal interaction amongst different bank users. The results reveals that people will continue using the four South African banks as long the aforesaid parameters are intensified.

Application of the Laplace Decomposition Method to Nonlinear Homogeneous and Non-Homogenous Advection Equations

2010 ◽  
Vol 65 (10) ◽  
pp. 849-853 ◽  
Author(s):  
Yasir Khan ◽  
Francis Austin
Keyword(s):  
Iteration Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Series Solutions ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Nonlinear Advection ◽  
Laplace Decomposition Method ◽  
Good Agreement

In this paper, we apply the Laplace decomposition method to obtain series solutions of nonlinear advection equations. The equations are Laplace transformed and the nonlinear terms are represented by Adomian polynomials. The results are in good agreement with those obtained by the Adomian decomposition method and the variational iteration method but the convergence is faster.

A New Approach to Van der Pol’s Oscillator Problem

2011 ◽  
Vol 66 (10-11) ◽  
pp. 620-624 ◽  
Author(s):  
Yasir Khan ◽  
M. Madani ◽  
A. Yildirim ◽  
M. A. Abdou ◽  
Naeem Faraz
Keyword(s):  
Numerical Method ◽  
Fourth Order ◽  
Decomposition Method ◽  
Nonlinear Oscillator ◽  
Adomian Decomposition Method ◽  
Series Solutions ◽  
New Approach ◽  
Adomian Decomposition ◽  
Highly Nonlinear ◽  
Laplace Decomposition Method

In this paper, we will consider the Laplace decomposition method (LDM) for finding series solutions of nonlinear oscillator differential equations. The equations are Laplace transformed and the nonlinear terms are represented by He’s polynomials. The solutions are compared with the numerical (fourth-order Runge-Kutta) solution and the solution obtained by the Adomian decomposition method. The suggested algorithm is more efficient and easier to handle as compared to the numerical method. The results illustrate that LDM is an appropriate method in solving the highly nonlinear equations.

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