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.

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 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.

Analytical Solution for the Subsurface Flow Wetland Model

2012 ◽  
Vol 198-199 ◽  
pp. 894-898
Author(s):  
Feng Lin Cheng
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Decomposition Method ◽  
Sewage Treatment ◽  
Subsurface Flow ◽  
Adomian Decomposition Method ◽  
Diffusion Characteristics ◽  
Adomian Decomposition ◽  
Laplace Transform Technique ◽  
The Laplace Transform

In this paper, the subsurface flow wetland sewage treatment mathematical model is studied. the analytical solution is obtained by using the Laplace transform technique for non-steady subsurface flow wetland model and the diffusion characteristics for some parameters used in the model are analyzed. Then the solution for the model which is added by the source is obtained on two boundary conditions by the adomian decomposition method. The examples are given compare the approximate solution and the exact solutions.

scholarly journals The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 780-785 ◽  
Author(s):  
Sunday O. Edeki ◽  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Grace O. Akinlabi
Keyword(s):  
Analytical Solution ◽  
Option Pricing ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Asian Option ◽  
Pricing Model ◽  
Adomian Decomposition ◽  
Option Pricing Model ◽  
Option Model ◽  
High Level

Abstract The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions are in good agreement with those of Rogers & Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani & Ahmad (ScienceAsia, 39S: 2013, 67–69). The proposed method is highly recommended for analytical solution of other forms of Asian option pricing models such as the geometric put and call options, even in their time-fractional forms. The basic Greeks obtained are the Theta, Delta, Speed, and Gamma which will be of great help to financial practitioners and traders in terms of hedging and strategy.

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