scholarly journals Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 791 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
Dian Chen Lu ◽  
Marjan Goodarzi
Keyword(s):  
Iteration Method ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Integral Transform ◽  
Integral Transformation ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Integral Transform Method

This study is about the lubrication of a long porous slider in which the fluid is injected into the porous bottom. The similarity transformation reduces the Navier-Stokes equations to couple nonlinear, ordinary differential equations, which are solved by a new algorithm. The proposed technique is based on integral transformation. Apparently, there is great symmetry between proposed method and variation iteration method, Adomian decomposition method but in integral transform method all the boundary conditions are applied, then a recursive scheme is used for the analytical solutions, which is unlike the Variational Iteration Method, Adomian Decomposition Method, and other existing analytical methods. Solutions are obtained for much larger Reynolds numbers, and they are compared with analytical and numerical methods. Effects of Reynolds number on velocity components are presented.

HPM AND VIM METHODS FOR FINDING THE EXACT SOLUTIONS OF THE NONLINEAR DISPERSIVE EQUATIONS AND SEVENTH-ORDER SAWADA–KOTERA EQUATION

2009 ◽  
Vol 23 (01) ◽  
pp. 39-52 ◽  
Author(s):  
D. D. GANJI ◽  
N. JAMSHIDI ◽  
Z. Z. GANJI
Keyword(s):  
Iteration Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Dispersive Equations ◽  
Nonlinear Dispersive Equations ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Seventh Order

In this paper, nonlinear dispersive equations and seventh-order Sawada–Kotera equation are solved using homotopy perturbation method (HPM) and variational iteration method (VIM). The results obtained by the proposed methods are then compared with that of Adomian decomposition method (ADM). The comparisons demonstrate that the two obtained solutions are in excellent agreement. The numerical results calculated show that the methods can be accurately implemented to these types of nonlinear equations. The results of HPM and VIM confirm the correctness of those obtained by Adomian decomposition method.

Solution of Fractional Diffusion Equation with a Moving Boundary Condition by Variational Iteration Method and Adomian Decomposition Method

2010 ◽  
Vol 65 (10) ◽  
pp. 793-799 ◽  
Author(s):  
Subir Das ◽  
Subir Rajeev
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Iteration Method ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Fractional Diffusion ◽  
Adomian Decomposition ◽  
Moving Boundary Condition

In this paper, the approximate analytic solutions of the mathematical model of time fractional diffusion equation (FDE) with a moving boundary condition are obtained with the help of variational iteration method (VIM) and Adomian decomposition method (ADM). By using boundary conditions, the explicit solutions of the diffusion front and fractional releases in the dimensionless form have been derived. Both mathematical techniques used to solve the problem perform extremely well in terms of efficiency and simplicity. Numerical solutions of the problem show that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

scholarly journals Numerical Simulation of the FitzHugh-Nagumo Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. A. Soliman
Keyword(s):  
Numerical Simulation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Nagumo Equations

The variational iteration method and Adomian decomposition method are applied to solve the FitzHugh-Nagumo (FN) equations. The two algorithms are illustrated by studying an initial value problem. The obtained results show that only few terms are required to deduce approximated solutions which are found to be accurate and efficient.

scholarly journals A New Reconstruction of Variational Iteration Method and Its Application to Nonlinear Volterra Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
K. Maleknejad ◽  
M. Tamamgar
Keyword(s):  
Exact Solution ◽  
Iteration Method ◽  
Decomposition Method ◽  
Solution Process ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Adomian Decomposition

We reconstruct the variational iteration method that we call, parametric iteration method (PIM). The purposed method was applied for solving nonlinear Volterra integrodifferential equations (NVIDEs). The solution process is illustrated by some examples. Comparisons are made between PIM and Adomian decomposition method (ADM). Also exact solution of the 3rd example is obtained. The results show the simplicity and efficiency of PIM. Also, the convergence of this method is studied in this work.

scholarly journals New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mohamed Z. Mohamed ◽  
Tarig M. Elzaki ◽  
Mohamed S. Algolam ◽  
Eltaib M. Abd Elmohmoud ◽  
Amjad E. Hamza
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Modified Method ◽  
Adomian Decomposition ◽  
Fractional Differential

The objective of this paper is to compute the new modified method of variational iteration and the Laplace Adomian decomposition method for the solution of nonlinear fractional partial differential equations. We execute a comparatively newfangled analytical mechanism that is denoted by the modified Laplace variational iteration method (MLVIM) and Laplace Adomian decomposition method (LADM). The effect of the numerical results indicates that the double approximation is handy to execute and reliable when applied. It is shown that numerical solutions are gained in the form of approximately series which are facilely computable.

scholarly journals A Comparative Study of VIM and ADM for Solving Volterra-Fredholm Integro-Differential Equations

2021 ◽  
Author(s):  
Ahmed Hamoud ◽  
Kirtiwant Ghadle
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Iteration Method ◽  
Existence And Uniqueness ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Adomian Decomposition

In this article, we present a comparative study between the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The study outlines the significant features of the two methods, for solving nonlinear Volterra-Fredholm integro-differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

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