scholarly journals Exact Solution for the Zakhrov-Kuzentsov Equation by Adomian Decomposition Method

2020 ◽  
pp. 1-11
Author(s):  
Fadlallah Mustafa Mosa ◽  
Eltayeb Abdellatif Mohamed Yousif
Keyword(s):  
Exact Solution ◽  
Acoustic Waves ◽  
Decomposition Method ◽  
Uniform Magnetic Field ◽  
Adomian Decomposition Method ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Zk Equation ◽  
Adomian Decomposition ◽  
Ion Acoustic

The Zakharov-kuznetsov equation (ZK-equation) governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and not isothermal electrons in the presence of a uniform magnetic field. This equation is a nonlinear equation. The main objective in this paper is to find an exact solution of ZK-equation using Adomain decomposition method. An exact solution of ZK(n,n,n) is derived by Adomain decomposition method. The solution of types ZK(2,2,2) and ZK(3,3,3) are presented in many examples to show the ability and efficiency of the method for ZK-equation. The solution is calculated in the form of convergent power series with easily computable components.

scholarly journals New computations for the two-mode version of the fractional Zakharov-Kuznetsov model in plasma fluid by means of the Shehu decomposition method

2021 ◽  
Vol 7 (2) ◽  
pp. 2044-2060
Author(s):  
Maysaa Al-Qurashi ◽  
◽  
Saima Rashid ◽  
Fahd Jarad ◽  
Madeeha Tahir ◽  
...  
Keyword(s):  
Exact Solution ◽  
Acoustic Waves ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Ion Acoustic ◽  
Sumudu Transforms

<abstract><p>In this research, the Shehu transform is coupled with the Adomian decomposition method for obtaining the exact-approximate solution of the plasma fluid physical model, known as the Zakharov-Kuznetsov equation (briefly, ZKE) having a fractional order in the Caputo sense. The Laplace and Sumudu transforms have been refined into the Shehu transform. The action of weakly nonlinear ion acoustic waves in a plasma carrying cold ions and hot isothermal electrons is investigated in this study. Important fractional derivative notions are discussed in the context of Caputo. The Shehu decomposition method (SDM), a robust research methodology, is effectively implemented to generate the solution for the ZKEs. A series of Adomian components converge to the exact solution of the assigned task, demonstrating the solution of the suggested technique. Furthermore, the outcomes of this technique have generated important associations with the precise solutions to the problems being researched. Illustrative examples highlight the validity of the current process. The usefulness of the technique is reinforced via graphical and tabular illustrations as well as statistics theory.</p></abstract>

scholarly journals Construction of an Approximate Analytical Solution for Multi-Dimensional Fractional Zakharov–Kuznetsov Equation via Aboodh Adomian Decomposition Method

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1542
Author(s):  
Saima Rashid ◽  
Khadija Tul Kubra ◽  
Juan Luis García Guirao
Keyword(s):  
Analytical Solution ◽  
Acoustic Waves ◽  
Decomposition Method ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Adomian Decomposition ◽  
Actual Solution ◽  
The Laplace Transform

In this paper, the Aboodh transform is utilized to construct an approximate analytical solution for the time-fractional Zakharov–Kuznetsov equation (ZKE) via the Adomian decomposition method. In the context of a uniform magnetic flux, this framework illustrates the action of weakly nonlinear ion acoustic waves in plasma carrying cold ions and hot isothermal electrons. Two compressive and rarefactive potentials (density fraction and obliqueness) are illustrated. With the aid of the Caputo derivative, the essential concepts of fractional derivatives are mentioned. A powerful research method, known as the Aboodh Adomian decomposition method, is employed to construct the solution of ZKEs with success. The Aboodh transform is a refinement of the Laplace transform. This scheme also includes uniqueness and convergence analysis. The solution of the projected method is demonstrated in a series of Adomian components that converge to the actual solution of the assigned task. In addition, the findings of this procedure have established strong ties to the exact solutions to the problems under investigation. The reliability of the present procedure is demonstrated by illustrative examples. The present method is appealing, and the simplistic methodology indicates that it could be straightforwardly protracted to solve various nonlinear fractional-order partial differential equations.

Propagation of dispersive wave solutions for (3 + 1)-dimensional nonlinear modified Zakharov–Kuznetsov equation in plasma physics

2020 ◽  
Vol 34 (25) ◽  
pp. 2050227
Author(s):  
Karmina K. Ali ◽  
Aly R. Seadawy ◽  
Asif Yokus ◽  
Resat Yilmazer ◽  
Hasan Bulut
Keyword(s):  
Magnetic Field ◽  
Acoustic Waves ◽  
Uniform Magnetic Field ◽  
Expansion Method ◽  
Dispersive Wave ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions ◽  
Proposed Model ◽  
Ion Acoustic

In the current study, we instigate the four-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation. The NLmZK equation guides the attitude of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Two different methods are used, namely the sine-Gordon expansion method (SGEM) and the [Formula: see text]-expansion method to the proposed model. We have successfully constructed some topological, non-topological, and wave solutions. In addition, the 2D, 3D, and contour graphs of the solutions are also plotted under the choice of appropriate values of the parameters.

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.

W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations

2021 ◽  
pp. 2150468
Author(s):  
Youssoufa Saliou ◽  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
M. S. Osman ◽  
Doka Serge Yamigno ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Singular Function ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Quantum Electron ◽  
Ion Acoustic ◽  
Trigonometric Function Solutions

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation.

scholarly journals Numerical solution of Drinfeld–Sokolov–Wilso system by using modified Adomian decomposition method

2021 ◽  
Vol 23 (1) ◽  
pp. 590
Author(s):  
Badran Jasim Salim ◽  
Oday Ahmed Jasim ◽  
Zeiad Yahya Ali
Keyword(s):  
Genetic Algorithm ◽  
Exact Solution ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Linear Partial Differential Equations ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Optimal Value ◽  
Mean Square Errors

<p class="Char">In this paper, the modified Adomian decomposition method (MADM) is usedto solve different types of differential equations, one of the numerical analysis methods for solving non linear partial differential equations (Drinfeld–Sokolov–Wilson system) and short (DSWS) that occur in shallow water flows. A Genetic Algorithm was used to find the optimal value for the parameter (a). We numerically solved the system (DSWS) and compared the result to the exact solution. When the value of it is low and close to zero, the MADM provides an excellent approximation to the exact solution. As well as the lower value of leads to the numerical algorithm of (MADM) approaching the real solution.  Finally, found the optimal value when a=-10 by using the Genetic Algorithm (G-MADM). All the computations were carried out with the aid of Maple 18 and Matlab to find the parameter value (a) by using the genetic algorithm as well as to figures drawing. The errors in this paper resulted from cut errors and mean square errors.</p>

scholarly journals Exact Solution of Space-Time Fractional Partial Differential Equations by Adomian Decomposition Method

2021 ◽  
pp. 75-87
Author(s):  
Vidya N. Bhadgaonkar ◽  
Bhausaheb R. Sontakke
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Decomposition Method ◽  
Graphical Representation ◽  
Adomian Decomposition Method ◽  
Physical Models ◽  
Partial Differential ◽  
Conduction Model ◽  
Adomian Decomposition ◽  
Present Technique

The intention behind this paper is to achieve exact solution of one dimensional nonlinear fractional partial differential equation(NFPDE) by using Adomian decomposition method(ADM) with suitable initial value. These equations arise in gas dynamic model and heat conduction model. The results show that ADM is powerful, straightforward and relevant to solve NFPDE. To represent usefulness of present technique, solutions of some differential equations in physical models and their graphical representation are done by MATLAB software.

Solution Non Linear Partial Differential Equations By ZMA Decomposition Method

2021 ◽  
Vol 20 ◽  
pp. 712-716
Author(s):  
Zainab Mohammed Alwan
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Integral Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Adomian Decomposition

In this survey, viewed integral transformation (IT) combined with Adomian decomposition method (ADM) as ZMA- transform (ZMAT) coupled with (ADM) in which said ZMA decomposition method has been utilized to solve nonlinear partial differential equations (NPDE's).This work is very useful for finding the exact solution of (NPDE's) and this result is more accurate obtained with compared the exact solution obtained in the literature.

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