scholarly journals Kamal Adomian Decomposition Method for Solving Nonlinear Wave-Like Equation with Variable Coefficients

2019 ◽  
pp. 1-11
Author(s):  
Azhari Ahmad
Keyword(s):  
Nonlinear Wave ◽  
Decomposition Method ◽  
Nonlinear Term ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Variable Coefficients ◽  
The Other ◽  
Transform Method ◽  
Adomian Polynomials ◽  
Adomian Decomposition

In this paper, we applied a new method for solving nonlinear wave-like equation with variable coefficients , when  the exact solution has a closed form. This method is Kamal Adomian De-composition Method (KADM). The Kamal decomposition method is a combined form of the Kamal transform method and the Adomian decomposition method [1,2,3]. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a significant advantage of this technique over the other methods. The results reveal that the Kamal decomposition method is very efficient, simple and can be applied to other nonlinear problems.

scholarly journals Fractional natural decomposition method for solving a certain class of nonlinear time-fractional wave-like equations with variable coefficients

2019 ◽  
Vol 11 (1) ◽  
pp. 99-116 ◽  
Author(s):  
Ali Khalouta ◽  
Abdelouahab Kadem
Keyword(s):  
Approximate Method ◽  
Decomposition Method ◽  
Nonlinear Term ◽  
Adomian Decomposition Method ◽  
Variable Coefficients ◽  
Transform Method ◽  
Adomian Polynomials ◽  
Clear Advantage ◽  
Adomian Decomposition ◽  
Natural Decomposition

Abstract In this paper, we propose a new approximate method, namely fractional natural decomposition method (FNDM) in order to solve a certain class of nonlinear time-fractional wave-like equations with variable coefficients. The fractional natural decomposition method is a combined form of the natural transform method and the Adomian decomposition method. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a clear advantage of this technique over the decomposition method. Some examples are given to illustrate the applicability and the easiness of this approach.

Adomian Decomposition Method for Approximating the Solutions of the Bidirectional Sawada-Kotera Equation

2010 ◽  
Vol 65 (8-9) ◽  
pp. 658-664 ◽  
Author(s):  
Xian-Jing Lai ◽  
Xiao-Ou Cai
Keyword(s):  
Decomposition Method ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Absolute Error ◽  
Solitary Wave Solutions ◽  
Adomian Polynomials ◽  
Wave Solutions ◽  
Adomian Decomposition

In this paper, the decomposition method is implemented for solving the bidirectional Sawada- Kotera (bSK) equation with two kinds of initial conditions. As a result, the Adomian polynomials have been calculated and the approximate and exact solutions of the bSK equation are obtained by means of Maple, such as solitary wave solutions, doubly-periodic solutions, two-soliton solutions. Moreover, we compare the approximate solution with the exact solution in a table and analyze the absolute error and the relative error. The results reported in this article provide further evidence of the usefulness of the Adomian decomposition method for obtaining solutions of nonlinear problems

scholarly journals Application of Sumudu Decomposition Method to Solve Nonlinear System Volterra Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hassan Eltayeb ◽  
Adem Kılıçman ◽  
Said Mesloub
Keyword(s):  
Decomposition Method ◽  
Close Agreement ◽  
Nonlinear Term ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Present Technique ◽  
Sumudu Transform

We develop a method to obtain approximate solutions for nonlinear systems of Volterra integrodifferential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled Volterra integrodifferential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of three examples and results of the present technique have close agreement with approximate solutions which were obtained with the help of Adomian decomposition method (ADM).

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.

Numerical solution of Lane-Emden type equations using Adomian decomposition method with unequal step-size partitions

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Umesh Umesh ◽  
Manoj Kumar
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Adomian Decomposition Method ◽  
The Other ◽  
Step Size ◽  
Adomian Polynomials ◽  
Content Type ◽  
Adomian Decomposition

Purpose The purpose of this paper is to obtain the highly accurate numerical solution of Lane–Emden-type equations using modified Adomian decomposition method (MADM) for unequal step-size partitions. Design/methodology/approach First, the authors describe the standard Adomian decomposition scheme and the Adomian polynomials for solving nonlinear differential equations. After that, for the fast calculation of the Adomian polynomials, an algorithm is presented based on Duan’s corollary and Rach’s rule. Then, MADM is discussed for the unequal step-size partitions of the domain, to obtain the numerical solution of Lane–Emden-type equations. Moreover, convergence analysis and an error bound for the approximate solution are discussed. Findings The proposed method removes the singular behaviour of the problems and provides the high precision numerical solution in the large effective region of convergence in comparison to the other existing methods, as shown in the tested examples. Originality/value Unlike the other methods, the proposed method does not require linearization or perturbation to obtain an analytical and numerical solution of singular differential equations, and the obtained results are more physically realistic.

scholarly journals Comment on “Adomian Decomposition Method for a Class of Nonlinear Problems”

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
S. Dalvandpour ◽  
A. Motamedinasab
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Adomian Decomposition

Sánchez Cano in his paper “Adomian Decomposition Method for a Class of Nonlinear Problems” in application part pages 8, 9, and 10 had made some mistakes in context; in this paper we correct them.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

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