scholarly journals Application of the Variational Iteration Method to Strongly Nonlinear -Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Hsuan-Ku Liu
Keyword(s):  
Approximate Solution ◽  
Time Scales ◽  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Results ◽  
Series Solutions ◽  
Nonlinear Difference Equations ◽  
Strongly Nonlinear ◽  
Variational Iteration

The theory of approximate solution lacks development in the area of nonlinear -difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two -polynomials are not easily found. In this paper, the formula for the multiplication of two -polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear -difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear -difference equations.

scholarly journals Variational Iteration Method forq-Difference Equations of Second Order

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Guo-Cheng Wu
Keyword(s):  
Lagrange Multiplier ◽  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Second Order ◽  
Iteration Formula ◽  
Strongly Nonlinear ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Oscillation Equation

Recently, Liu extended He's variational iteration method to strongly nonlinearq-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. Theq-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.

scholarly journals The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Constant Coefficients

Variational iteration method and homotopy perturbation method are used to solve the fractional Fredholm integrodifferential equations with constant coefficients. The obtained results indicate that the method is efficient and also accurate.

scholarly journals Variational Iteration Method for Solving the Generalized Degasperis-Procesi Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qian Lijuan ◽  
Tian Lixin ◽  
Ma Kaiping
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Initial Approximation ◽  
Variational Iteration Method ◽  
Original Equation ◽  
Variational Iteration

We introduce the variational iteration method for solving the generalized Degasperis-Procesi equation. Firstly, according to the variational iteration, the Lagrange multiplier is found after making the correction functional. Furthermore, several approximations ofun+1(x,t)which is converged tou(x,t)are obtained, and the exact solutions of Degasperis-Procesi equation will be obtained by using the traditional variational iteration method with a suitable initial approximationu0(x,t). Finally, after giving the perturbation item, the approximate solution for original equation will be expressed specifically.

scholarly journals Approximate Solution of Linear Fuzzy Initial Value Problems Using Modified Variaional Iteration Method

2021 ◽  
Vol 24 (4) ◽  
pp. 32-39
Author(s):  
Hussein M. Sagban ◽  
◽  
Fadhel S. Fadhel ◽  
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

The main objective of this paper is to solve fuzzy initial value problems, in which the fuzziness occurs in the initial conditions. The proposed approach, namely the modified variational iteration method, will be used to find the solution of fuzzy initial value problem approximately and to increase the rate of convergence of the variational iteration method. From the obtained results, as it is expected, the approximate results of the proposed method are more accurate than those results obtained without using the modified variational iteration method.

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.

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