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.

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 A New Solution of Time-Fractional Coupled KdV Equation by Using Natural Decomposition Method

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Elbadri ◽  
Shams A. Ahmed ◽  
Yahya T. Abdalla ◽  
Walid Hdidi
Keyword(s):  
Decomposition Method ◽  
Kdv Equation ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Coupled Kdv Equation ◽  
A New Technique ◽  
Natural Decomposition ◽  
Made In

In this article, we applied a new technique for solving the time-fractional coupled Korteweg-de Vries (KdV) equation. This method is a combination of the natural transform method with the Adomian decomposition method called the natural decomposition method (NDM). The solutions have been made in a convergent series form. To demonstrate the performances of the technique, two examples are provided.

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).

scholarly journals Natural Decomposition Approximation Solution for First Order Nonlinear Differential Equations

2018 ◽  
Vol 7 (4.5) ◽  
pp. 442
Author(s):  
A. Patra ◽  
T. T. Shone ◽  
B. B. Mishra
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Adomian Decomposition Method ◽  
Approximation Solution ◽  
Transform Method ◽  
First Order ◽  
Adomian Decomposition ◽  
Natural Decomposition ◽  
First Order Differential Equations

In this research paper, we propose the Natural decomposition method (NDM) to solve nonlinear first order differential equations. We compare the results obtained by NDM with the exact solutions. This method is a combination of the natural transform method and adomian decomposition method. By showing the less error one can be concluded that the NDM is easy to use and efficient.  

scholarly journals Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4389-4401 ◽  
Author(s):  
Hassan Gadain
Keyword(s):  
Decomposition Method ◽  
Boussinesq Equation ◽  
Adomian Decomposition Method ◽  
Boussinesq Equations ◽  
Science And Engineering ◽  
Transform Method ◽  
One Dimensional ◽  
Adomian Decomposition ◽  
Linear And Nonlinear ◽  
Natural Decomposition

In this work, a combined form of the double Natural transform method with the Adomian decomposition method is developed for analytic treatment of the linear and nonlinear singular one dimensional Boussinesq equations. Two examples are provided to illustrate the simplicity and reliability of this method. Moreover, the results show that the proposed method is effective and is easy to implement for certain problems in science and engineering.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

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.

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

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