scholarly journals Variational Iteration Method for the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Lan Xu ◽  
Eric W. M. Lee
Keyword(s):  
Boundary Layer ◽  
Iteration Method ◽  
Stretching Sheet ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Magnetohydrodynamic Flow ◽  
Boundary Layer Problem ◽  
Variational Iteration ◽  
Nonlinear Stretching ◽  
Layer Problem

The variational iteration method (VIM) is applied to solve the boundary layer problem of magnetohydrodynamic flow over a nonlinear stretching sheet. The combination of the VIM and the Padé approximants is shown to be a powerful method for solving two-point boundary value problems consisting of systems of nonlinear differential equations. And the comparison of the obtained results with other available results shows that the method is very effective and convenient for solving boundary layer problems.

A NEWLY MODIFIED VARIATIONAL ITERATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350029
Author(s):  
R. YULITA MOLLIQ ◽  
M. S. M. NOORANI
Keyword(s):  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Method Comparison ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Accurate Method ◽  
Convergence Region ◽  
Variational Iteration ◽  
Approximate Analytical Solutions ◽  
Modified Variational Iteration Method

This paper presents a new reliable modification of the variational iteration method (MoVIM). An enlarged interval of convergence region of series solutions is obtained by inserting a nonzero auxiliary parameter (ℏ) into the correction functional of variational iteration method. Approximate analytical solutions for some examples of nonlinear problems are obtained using variational iteration method. Comparison with the exact solution, Runge–Kutta method 4, and also another modified variational iteration method has shown that MoVIM is an accurate method for solving nonlinear problems.

Application of Variational Iteration Method in Nonlinear Free Vibration Analysis of Multi-Layered Nano-Scale Graphene Sheets

2014 ◽  
Author(s):  
Mehran Sadri ◽  
Davood Younesian ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Free Vibration ◽  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Free Vibration Analysis ◽  
Variational Iteration Method ◽  
Graphene Sheets ◽  
Geometrical Parameters ◽  
Nonlinear Free Vibration ◽  
Variational Iteration ◽  
Nano Scale

The nonlinear free vibration of multi-layered nano-scale graphene sheets is studied. Using the von Kármán and nonlocal continuum theories, large amplitude of vibration is included in the analysis as well as the size effect of nano-structure. The SSSS boundary condition is considered for the multi-layered graphene sheet and coupled nonlinear differential equations of motion of layers are taken into account based on Galerkin method. Variational iteration method (VIM) is employed as the solution procedure and nonlinear natural frequencies of the system are analytically determined. Two different geometries are taken into account and the analytical results are compared with frequencies obtained by numerical method. Finally, influence of geometrical parameters and amplitude of vibration on nonlinear frequencies of the system is examined.

scholarly journals New analytical solution for natural convection of Darcian fluid in porous media prescribed surface heat flux

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 221-227 ◽  
Author(s):  
Domiry Ganji ◽  
Hasan Sajjadi
Keyword(s):  
Heat Flux ◽  
Porous Media ◽  
Differential Equations ◽  
Iteration Method ◽  
Surface Heat Flux ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Surface Heat ◽  
Variational Iteration ◽  
He’S Variational Iteration Method

A new analytical method called He's Variational Iteration Method is introduced to be applied to solve nonlinear equations. In this method, general Lagrange multipliers are introduced to construct correction functional for the problems. It is strongly and simply capable of solving a large class of linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term and also is very user friend because it reduces the size of calculations besides; its iterations are direct and straightforward. In this paper the powerful method called Variational Iteration Method is used to obtain the solution for a nonlinear Ordinary Differential Equations that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. The obtained Variational Iteration Method solution in comparison with the numerical ones represents a remarkable accuracy.

Variational iteration method with He's polynomials for MHD Falkner-Skan flow over permeable wall based on Lie symmetry method

2014 ◽  
Vol 24 (6) ◽  
pp. 1348-1362 ◽  
Author(s):  
Buhe Eerdun ◽  
Qiqige Eerdun ◽  
Bala Huhe ◽  
Chaolu Temuer ◽  
Jing-Yu Wang
Keyword(s):  
Boundary Layer ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Lie Symmetry ◽  
Content Type ◽  
Variational Iteration ◽  
Lie Symmetry Method ◽  
He’S Polynomials ◽  
Layer Flow ◽  
Symmetry Method

Purpose – The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field. Design/methodology/approach – The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials. Findings – The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems. Originality/value – In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.

scholarly journals Modified Variational Iteration Method for Free-Convective Boundary-Layer Equation Using Padé Approximation

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yildirim ◽  
Sefa Anıl Sezer ◽  
Muhammad Usman
Keyword(s):  
Boundary Layer ◽  
Convective Boundary Layer ◽  
Iteration Method ◽  
Padé Approximation ◽  
Boundary Layer Equation ◽  
Variational Iteration Method ◽  
Pade Approximation ◽  
Convective Boundary ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

This paper is devoted to the study of a free-convective boundary-layer flow modeled by a system of nonlinear ordinary differential equations. We apply a modified variational iteration method (MVIM) coupled with He's polynomials and Padé approximation to solve free-convective boundary-layer equation. It is observed that the combination of MVIM and the Padé approximation improves the accuracy and enlarges the convergence domain.

scholarly journals Solution of Space-Time-Fractional Problem by Shehu Variational Iteration Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Suleyman Cetinkaya ◽  
Ali Demir ◽  
Hulya Kodal Sevindir
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Space Time ◽  
Variational Iteration ◽  
Mathematical Problems ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

In this study, we deal with the problem of constructing semianalytical solution of mathematical problems including space-time-fractional linear and nonlinear differential equations. The method, called Shehu Variational Iteration Method (SVIM), applied in this study is a combination of Shehu transform (ST) and variational iteration method (VIM). First, ST is utilized to reduce the time-fractional differential equation with fractional derivative in Liouville-Caputo sense into an integer-order differential equation. Later, VIM is implemented to construct the solution of reduced differential equation. The convergence analysis of this method and illustrated examples confirm that the proposed method is one of best procedures to tackle space-time-fractional differential equations.

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