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 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.

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 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.

MHD Natural Convection Slip Flow through Vertical Porous Plates with Time-Periodic Boundary Conditions

2018 ◽  
Vol 388 ◽  
pp. 135-145
Author(s):  
Samuel Olumide Adesanya ◽  
L. Rundora ◽  
R.S. Lebelo ◽  
K.C. Moloi
Keyword(s):  
Convective Flow ◽  
Decomposition Method ◽  
Hartmann Number ◽  
Slip Flow ◽  
Adomian Decomposition Method ◽  
Periodic Boundary Conditions ◽  
Temperature Profiles ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Time Periodic

In this work, the convective flow of heat generating hydromagnetic fluid through a leaky channel is investigated. Due to channel porosity, the asymmetrical slip conditions are imposed on both walls. The coupled dimensionless partial differential equations are reduced to a system of second-order boundary-value problems based on some flow assumptions and solved by Adomian decomposition method (ADM). Variations in velocity and temperature profiles are presented and discussed in detail. The result of the analysis revealed that increasing Hartmann number decreases the flow velocity while the slip parameters enhance the flow.

An Approximate Solution of Muijderman's Model for Performance Calculation of Spiral Grooved Gas Seal

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Wanjun Xu ◽  
Jiangang Yang
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Kutta Method ◽  
Film Pressure ◽  
Runge Kutta Method ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Runge Kutta ◽  
Performance Calculation

This paper presents an approximate solution of Muijderman's model for compressible spiral grooved gas film. The approximate solution is derived from Muijderman's equations by Adomian decomposition method. The obtained approximate solution expresses the gas film pressure as a function of the gas film radius. The traditional Runge–Kutta method is avoided. The accuracy of the approximate solution is acceptable, and it brings convenience for performance calculation of spiral grooved gas seal. A complete Adomian decomposition procedure of Muijderman's equations is presented. The approximate solution is validated with published results.

scholarly journals Solvability of the p-adic Analogue of Navier–Stokes Equation via the Wavelet Theory

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1129 ◽  
Author(s):  
Ehsan Pourhadi ◽  
Andrei Khrennikov ◽  
Reza Saadati ◽  
Klaudia Oleschko ◽  
María de Jesús Correa Correa Lopez
Keyword(s):  
Stokes Equation ◽  
Random Media ◽  
Adomian Decomposition Method ◽  
Navier Stokes ◽  
Dynamical Equations ◽  
Navier Stokes Equation ◽  
Oil Emulsion ◽  
Capillary Networks ◽  
Biological Phenomena ◽  
Adomian Decomposition

P-adic numbers serve as the simplest ultrametric model for the tree-like structures arising in various physical and biological phenomena. Recently p-adic dynamical equations started to be applied to geophysics, to model propagation of fluids (oil, water, and oil-in-water and water-in-oil emulsion) in capillary networks in porous random media. In particular, a p-adic analog of the Navier–Stokes equation was derived starting with a system of differential equations respecting the hierarchic structure of a capillary tree. In this paper, using the Schauder fixed point theorem together with the wavelet functions, we extend the study of the solvability of a p-adic field analog of the Navier–Stokes equation derived from a system of hierarchic equations for fluid flow in a capillary network in porous medium. This equation describes propagation of fluid’s flow through Geo-conduits, consisting of the mixture of fractures (as well as fracture’s corridors) and capillary networks, detected by seismic as joint wave/mass conducts. Furthermore, applying the Adomian decomposition method we formulate the solution of the p-adic analog of the Navier–Stokes equation in term of series in general form. This solution may help researchers to come closer and find more facts, taking into consideration the scaling, hierarchies, and formal derivations, imprinted from the analogous aspects of the real world phenomena.

scholarly journals Adomian Decomposition Method for a Class of Nonlinear Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
J. A. Sánchez Cano
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Coupled System ◽  
Nonlinear Ordinary Differential Equations ◽  
Adomian Decomposition

The Adomian decomposition method together with some properties of nested integrals is used to provide a solution to a class of nonlinear ordinary differential equations and a coupled system.

Application of Adomian Decomposition Method on a Mathematical Model of Malaria

2020 ◽  
pp. 417-435
Author(s):  
Adesoye Idowu Abioye ◽  
Olumuyiwa James Peter ◽  
Ayotunde Abayomi Ayoade ◽  
Ohigweren Airenoni Uwaheren ◽  
Mohammed Olanrewaju Ibrahim
Keyword(s):  
Mathematical Model ◽  
Fourth Order ◽  
Decomposition Method ◽  
Deterministic Model ◽  
Adomian Decomposition Method ◽  
Model Solution ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Malaria Model

In this paper, we consider a deterministic model of malaria transmission. Adomian decomposition method (ADM) is used to calculate an approximation to the solution of the non-linear couple of differential equations governing the model. Classical fourth-order Runge-Kutta method implemented in Maple18 confirms the validity of the ADM in solving the problem. Graphical results show that ADM agrees with R-K 4. In order words, these produced the same behaviour, validating ADM's efficiency and accuracy of ADM in finding the malaria model solution.

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