A new method for calculating general lagrange multiplier in the variational iteration method

2011 ◽  
Vol 27 (4) ◽  
pp. 996-1001 ◽  
Author(s):  
Hossein Jafari ◽  
Abbas Alipoor
Keyword(s):  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
New Method ◽  
Variational Iteration

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 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 A General Iteration Formula of VIM for Fractional Heat- and Wave-Like Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Fukang Yin ◽  
Junqiang Song ◽  
Xiaoqun Cao
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Iteration Formula ◽  
Variational Iteration

A general iteration formula of variational iteration method (VIM) for fractional heat- and wave-like equations with variable coefficients is derived. Compared with previous work, the Lagrange multiplier of the method is identified in a more accurate way by employing Laplace’s transform of fractional order. The fractional derivative is considered in Jumarie’s sense. The results are more accurate than those obtained by classical VIM and the same as ADM. It is shown that the proposed iteration formula is efficient and simple.

scholarly journals On the Computation of the Lagrange Multiplier for the Variational Iteration Method (VIM) for Solving Differential Equations

2020 ◽  
pp. 74-92
Author(s):  
N. Okiotor ◽  
F. Ogunfiditimi ◽  
M. O. Durojaye
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Integrating Factor ◽  
Variational Iteration ◽  
Approximate Result ◽  
Number Of Iterations

In this study, the Variational Iteration Method (VIM) is applied in finding the solution of differential equations with emphasis laid on the choice of the Lagrange multiplier used while employing VIM. Building on existing methods and variational theories, the operator D-Method and integrating factor are employed in certain aspects in the determination of exact Lagrange multiplier for VIM. When results of the computed exact Lagrange multiplier were compared with results of approximate Lagrange multiplier, it was observed that the computed exact Lagrange multiplier reduced significantly the number of iterations required to get a good approximate result, and in some cases the result converged to the exact solution after a single iteration. Evaluations are carried out using MAPLE Software.

scholarly journals A Hybrid Modified Approach for Solving Fuzzy Differential Equations

2017 ◽  
Vol 5 (2) ◽  
Author(s):  
Alauldeen N. Ahmad ◽  
Basma A. Nema
Keyword(s):  
Differential Equations ◽  
Lagrange Multiplier ◽  
Hybrid Method ◽  
Iteration Method ◽  
Laplace Transformation ◽  
Variational Iteration Method ◽  
Ranking Method ◽  
Lower Upper ◽  
Variational Iteration ◽  
Fuzzy Parameters

In this paper, a hybrid method is presented by combining Laplace transformation and variational iteration method for solving fuzzy differential equations with fuzzy initial and boundaries values. A defuzzification technique had been implemented to convert the fuzzy parameters into crisp values by building an extended ranking method. Then the method is implemented on the new problem in which two approaches has been built according to the formula of  Lagrange multiplier obtaining the lower, upper and center solutions.

scholarly journals On the Solution of Generalized Space Time Fractional Telegraph Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Badr S. Alkahtani ◽  
Vartika Gulati ◽  
Pranay Goswami
Keyword(s):  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Telegraph Equation ◽  
Space Time ◽  
New Technique ◽  
Variational Iteration ◽  
Fractional Telegraph Equation ◽  
Sumudu Transform

We present the solution of generalized space time fractional telegraph equation by using Sumudu variational iteration method which is the combination of variational iteration method and Sumudu transform. We tried to overcome the difficulties in finding the value of Lagrange multiplier by this new technique.

scholarly journals The variational iteration method for solving the Volterra integro-differential forms of the Lane-Emden and the Emden-Fowler problems with initial and boundary value conditions

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz ◽  
Suheil A. Khuri
Keyword(s):  
Boundary Value Problems ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Boundary Value ◽  
Differential Forms ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Shape Factors ◽  
Variational Iteration

AbstractIn this paper, the variational iteration method (VIM) is used to examine the Volterra integro-differential forms of the singular Lane–Emden and the Emden–Fowler initial value problems and boundary value problems arising in physics, astrophysics and stellar structures. The Volterra integro-differential forms of the Lane–Emden and the Emden–Fowler equations overcome the singularity behavior at the origin x = 0. The Lagrange multiplier, needed for the VIM, is λ = −1 for the various cases of the specified equations having distinct shape factors. We illustrate our work by analyzing few initial value problems and boundary value problems to emphasize the convergence of the acquired results.

Variational Iteration Method for Burgers’ and Coupled Burgers’ Equations Using He’s Polynomials

2010 ◽  
Vol 65 (4) ◽  
pp. 263-267 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Lagrange Multiplier ◽  
Iteration Method ◽  
Decomposition Method ◽  
Variational Iteration Method ◽  
Burgers Equations ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
Proposed Modification

In this paper, we apply a modified version of the variational iteration method (MVIM) for solving Burgers’ and coupled Burgers’ equations. The proposed modification is made by introducing He’s polynomials in the correction functional of the variational iteration method (VIM). The use of Lagrange multiplier coupled with He’s polynomials are the clear advantages of this technique over the decomposition method.

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