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 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 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 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.  

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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.

scholarly journals On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668653 ◽  
Author(s):  
Hassan Eltayeb Gadain ◽  
Imed Bachar
Keyword(s):  
Parabolic Equation ◽  
Laplace Transform ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 949 ◽  
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub ◽  
Yahya T. Abdalla ◽  
Adem Kılıçman
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Laplace Decomposition Method

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the efficiency, high accuracy, and the simplicity of present method.

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