scholarly journals A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

scholarly journals Laplace Adomian Decomposition Method for Multi Dimensional Time Fractional Model of Navier-Stokes Equation

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 149 ◽  
Author(s):  
Shahid Mahmood ◽  
Rasool Shah ◽  
Hassan khan ◽  
Muhammad Arif
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Stokes Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
The Given

In this research paper, a hybrid method called Laplace Adomian Decomposition Method (LADM) is used for the analytical solution of the system of time fractional Navier-Stokes equation. The solution of this system can be obtained with the help of Maple software, which provide LADM algorithm for the given problem. Moreover, the results of the proposed method are compared with the exact solution of the problems, which has confirmed, that as the terms of the series increases the approximate solutions are convergent to the exact solution of each problem. The accuracy of the method is examined with help of some examples. The LADM, results have shown that, the proposed method has higher rate of convergence as compare to ADM and HPM.

scholarly journals Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

2019 ◽  
Vol 24 (1) ◽  
pp. 7 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Asmaa Al-Enazi ◽  
Bassam Z. Albalawi ◽  
Mona D. Aljoufi
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Surface Brightness ◽  
Milky Way ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Canonical Forms ◽  
Exponential Functions ◽  
Adomian Decomposition ◽  
Delay Differential

The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided in the form of a power series which agrees with the solution in the literature, while the second expresses the solution in terms of exponential functions which is viewed as a new solution. A rapid rate of convergence has been achieved and displayed in several graphs. Furthermore, only a few terms of the new approximate solution (expressed in terms of exponential functions) are sufficient to achieve extremely accurate numerical results when compared with a large number of terms of the first solution in the literature. In addition, the residual error using a few terms approaches zero as the delay parameter increases, hence, this confirms the effectiveness of the present approach over the solution in the literature.

Numerical Solution of Time Fractional Navier-Stokes Equation by Discrete Adomian decomposition method

2014 ◽  
Vol 3 (1) ◽  
pp. 21-26 ◽  
Author(s):  
Gunvant A. Birajdar
Keyword(s):  
Exact Solution ◽  
Numerical Solution ◽  
Stokes Equation ◽  
Decomposition Method ◽  
Graphical Representation ◽  
Adomian Decomposition Method ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Space Domain ◽  
Adomian Decomposition

AbstractIn this paper we find the solution of time fractional discrete Navier-Stokes equation using Adomian decomposition method. Here we discretize the space domain. The graphical representation of solution given by using Matlab software, and it compared with exact solution for alpha = 1.

scholarly journals Analytical Approximate Solution of Nonlinear Differential Equation Governing Jeffery-Hamel Flow with High Magnetic Field by Adomian Decomposition Method

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
D. D. Ganji ◽  
M. Sheikholeslami ◽  
H. R. Ashorynejad
Keyword(s):  
Decomposition Method ◽  
Hartmann Number ◽  
Adomian Decomposition Method ◽  
Navier Stokes ◽  
Nonlinear Ordinary Differential Equations ◽  
Governing Equations ◽  
Navier Stokes Equation ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Divergent Channel

The magnetohydrodynamic Jeffery-Hamel flow is studied analytically. The traditional Navier-Stokes equation of fluid mechanics and Maxwell's electromagnetism governing equations reduce to nonlinear ordinary differential equations to model this problem. The analytical tool of Adomian decomposition method is used to solve this nonlinear problem. The velocity profile of the conductive fluid inside the divergent channel is studied for various values of Hartmann number. Results agree well with the numerical (Runge-Kutta method) results, tabulated in a table. The plots confirm that the method used is of high accuracy for different α, Ha, and Re numbers.

scholarly journals Three-Dimensional Laplace Adomian Decomposition Method and Singular Pseudoparabolic Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Hassan Eltayeb ◽  
Diaa Eldin Elgezouli ◽  
Adem Kilicman ◽  
Imed Bachar
Keyword(s):  
Approximate Solution ◽  
Numerical Analysis ◽  
Decomposition Method ◽  
Three Dimensional ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Two Dimensional ◽  
Pseudoparabolic Equation ◽  
Adomian Decomposition ◽  
Pseudoparabolic Equations

In this work, the solution of the linear, nonlinear, and coupled system fractional singular two-dimensional pseudoparabolic equation is examined by using a three-dimensional Laplace Adomian decomposition method (3-DLADM). Analysis of the method is discussed, and some demonstrative examples are mentioned to confirm the power and accuracy of the recommended method, and numerical analysis is applied to sketch the exact and approximate solution.

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 Numerical Simulation of Cubic-Quartic Optical Solitons with Perturbed Fokas–Lenells Equation Using Improved Adomian Decomposition Algorithm

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 138
Author(s):  
Alyaa A. Al-Qarni ◽  
Huda O. Bakodah ◽  
Aisha A. Alshaery ◽  
Anjan Biswas ◽  
Yakup Yıldırım ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Iterative Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Numerical Results ◽  
Decomposition Algorithm ◽  
Adomian Decomposition ◽  
High Level ◽  
Do So

The current manuscript displays elegant numerical results for cubic-quartic optical solitons associated with the perturbed Fokas–Lenells equations. To do so, we devise a generalized iterative method for the model using the improved Adomian decomposition method (ADM) and further seek validation from certain well-known results in the literature. As proven, the proposed scheme is efficient and possess a high level of accuracy.

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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