scholarly journals An Aproximation to Solution of Space and Time Fractional Telegraph Equations by the Variational Iteration Method

2012 ◽  
Vol 2012 ◽  
pp. 1-2 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Effective Algorithm ◽  
Variational Iteration ◽  
Space And Time ◽  
Telegraph Equations

Sevimlican suggested an effective algorithm for space and time fractional telegraph equations by the variational iteration method. This paper shows that algorithm can be updated by either variational iteration algorithm-II or the fractional variational iteration method.

scholarly journals An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Sevimlican
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Space And Time ◽  
Telegraph Equations ◽  
He’S Variational Iteration Method

He's variational iteration method (VIM) is used for solving space and time fractional telegraph equations. Numerical examples are presented in this paper. The obtained results show that VIM is effective and convenient.

scholarly journals Comment on “An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method”

2013 ◽  
Vol 2013 ◽  
pp. 1-2
Author(s):  
Yi-Hong Wang ◽  
Lan-Lan Huang
Keyword(s):  
Laplace Transform ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Telegraph Equation ◽  
Variational Iteration ◽  
Space And Time ◽  
Fractional Telegraph Equation ◽  
Telegraph Equations ◽  
He’S Variational Iteration Method

The variational iteration method was applied to the time fractional telegraph equation and some variational iteration formulae were suggested in (Sevimlican, 2010). Those formulae are improved by Laplace transform from which the approximate solutions of higher accuracies can be obtained.

scholarly journals The local fractional variational iteration method a promising technology for fractional calculus

2020 ◽  
Vol 24 (4) ◽  
pp. 2605-2614 ◽  
Author(s):  
Yong-Ju Yang
Keyword(s):  
Fractional Calculus ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Initial Solution ◽  
Iteration Algorithm ◽  
Promising Technology ◽  
Variational Iteration ◽  
Sumudu Transform

In order to make the local variational iteration algorithm converge faster and more effective, the Sumudu transform is adopted and a proper initial solution is chosen. Some examples are given to show that the presented method is reliable, efficient and easy to implement from a computational viewpoint.

scholarly journals A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fatima A. Alawad ◽  
Eltayeb A. Yousif ◽  
Arbab I. Arbab
Keyword(s):  
Laplace Transform ◽  
Exact Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Space Time ◽  
New Techniques ◽  
Variational Iteration ◽  
Telegraph Equations ◽  
A New Technique ◽  
Special Case

In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders.

An Alternative Approach to Differential-Difference Equations Using the Variational Iteration Method

2010 ◽  
Vol 65 (12) ◽  
pp. 1055-1059 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
Francis Austin
Keyword(s):  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Mathematical Tool ◽  
Variational Iteration ◽  
Alternative Approach

Although a variational iteration algorithm was proposed by Yildirim (Math. Prob. Eng. 2008 (2008), Article ID 869614) that successfully solves differential-difference equations, the method involves some repeated and unnecessary iterations in each step. An alternative iteration algorithm (variational iteration algorithm-II) is constructed in this paper that overcomes this shortcoming and promises to provide a universal mathematical tool for many differential-difference equations.

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.

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