Variational Iteration Method for the Magneto-Hydrodynamic Nanoflow Over a Nonlinear Stretching Sheet Using He's Polynomials

2012 ◽  
Vol 10 (1) ◽  
pp. 635-639 ◽  
Author(s):  
Eerdun Buhe ◽  
Temuer Chaolu ◽  
Jing Pang
Keyword(s):  
Iteration Method ◽  
Stretching Sheet ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
Nonlinear Stretching

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.

scholarly journals Solitary and compacton solutions of fractional KdV-like equations

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 328-336 ◽  
Author(s):  
Bo Tang ◽  
Yingzhe Fan ◽  
Jianping Zhao ◽  
Xuemin Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Reliable Tool ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
Liouville Derivative

AbstractIn this paper, based on Jumarie’s modified Riemann-Liouville derivative, we apply the fractional variational iteration method using He’s polynomials to obtain solitary and compacton solutions of fractional KdV-like equations. The results show that the proposed method provides a very effective and reliable tool for solving fractional KdV-like equations, and the method can also be extended to many other fractional partial differential equations.

Variational Iteration Method for the Hirota-Satsuma Model Using He’s Polynomials

2010 ◽  
Vol 65 (6-7) ◽  
pp. 525-528 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yildirim
Keyword(s):  
Applied Sciences ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Results ◽  
Variational Iteration ◽  
He’S Polynomials

This paper out lines the implementation of the variational iteration method using He’s polynomials (VMHP) for solving the Hirota-Satsuma model which occurs quite often in applied sciences. Numerical results show that the proposed VIMHP is quite efficient.

scholarly journals Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials

2010 ◽  
Vol 2010 ◽  
pp. 1-28 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yildirim ◽  
M. M. Hosseini
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
User Friendly

This paper outlines a detailed study of the coupling of He's polynomials with correction functional of variational iteration method (VIM) for solving various initial and boundary value problems. The elegant coupling gives rise to the modified versions of VIM which is very efficient in solving nonlinear problems of diversified nature. It is observed that the variational iteration method using He's polynomials (VIMHP) is very efficient, easier to implements, and more user friendly. Several examples are given to reconfirm the efficiency of the proposed VIMHP.

scholarly journals Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials”

2012 ◽  
Vol 2012 ◽  
pp. 1-2 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Initial Boundary ◽  
Iteration Algorithm ◽  
Initial Boundary Value Problems ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
Fractional Differential ◽  
Initial Boundary Value ◽  
Modified Variational Iteration Method

Recently Liu applied the variational homotopy perturbation method for fractional initial boundary value problems. This note concludes that the method is a modified variational iteration method using He’s polynomials. A standard variational iteration algorithm for fractional differential equations is suggested.

Modified Variational Iteration Method for Integro-Differential Equations and Coupled Systems

2010 ◽  
Vol 65 (4) ◽  
pp. 277-284 ◽  
Author(s):  
Syed Tauseef Mohyud-Din
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Coupled Systems ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
Proposed Modification ◽  
Adomian’S Polynomials ◽  
Modified Variational Iteration Method

In this paper, we apply the modified variational iteration method (mVIM) for solving integrodifferential equations and coupled systems of integro-differential equations. The proposed modification is made by the elegant coupling of He’s polynomials and the correction functional of variational iteration method. The proposed mVIM is applied without any discretization, transformation or restrictive assumptions and is free from round off errors and calculation of the so-called Adomian’s polynomials.

Sign in / Sign up

Export Citation Format

Share Document