scholarly journals Variational iteration method for solving the space- and time-fractional KdV equation

2007 ◽  
Vol 24 (1) ◽  
pp. 262-271 ◽  
Author(s):  
Shaher Momani ◽  
Zaid Odibat ◽  
Ahmed Alawneh
Keyword(s):  
Iteration Method ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Space And Time

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 An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Hakeem Ullah ◽  
Saeed Islam ◽  
Muhammad Idrees ◽  
Mehreen Fiza ◽  
Zahoor Ul Haq
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Asymptotic Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Optimal Homotopy Asymptotic Method

We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM). We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM) and homotopy perturbation method (HPM) solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

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 Analytical approach to a generalized Hirota-Satsuma coupled Korteweg-de Vries equation by modified variational iteration method

2016 ◽  
Vol 20 (3) ◽  
pp. 885-888 ◽  
Author(s):  
Jun-Feng Lu ◽  
Li Ma
Keyword(s):  
Iteration Method ◽  
Analytical Approach ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
De Vries ◽  
Modified Variational Iteration Method

In this paper, we apply the modified variational iteration method to a generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation. The numerical solutions of the initial value problem of the generalized Hirota-Satsuma coupled KdV equation are provided. Numerical results are given to show the efficiency of the modified variational iteration method.

scholarly journals Active Optimal Control of the KdV Equation Using the Variational Iteration Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Iteration Method ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Control Variable ◽  
Variational Iteration Method ◽  
Performance Measure ◽  
Quadratic Functional ◽  
Variational Iteration ◽  
The Kdv Equation

The optimal pointwise control of the KdV equation is investigated with an objective of minimizing a given performance measure. The performance measure is specified as a quadratic functional of the final state and velocity functions along with the energy due to open- and closed-loop controls. The minimization of the performance measure over the controls is subjected to the KdV equation with periodic boundary conditions and appropriate initial condition. In contrast to standard optimal control or variational methods, a direct control parameterization is used in this study which presents a distinct approach toward the solution of optimal control problems. The method is based on finite terms of Fourier series approximation of each time control variable with unknown Fourier coefficients and frequencies. He's variational iteration method for the nonlinear partial differential equations is applied to the problem and thus converting the optimal control of lumped parameter systems into a mathematical programming. A numerical simulation is provided to exemplify the proposed method.

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