Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order

2006 ◽  
Vol 7 (1) ◽  
Author(s):  
Ζ.Μ. Odibat ◽  
S. Momani
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Variational Iteration

scholarly journals Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Iteration Method ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Variational Iteration

We are concerned here with singular partial differential equations of fractional order (FSPDEs). The variational iteration method (VIM) is applied to obtain approximate solutions of this type of equations. Convergence analysis of the VIM is discussed. This analysis is used to estimate the maximum absolute truncated error of the series solution. A comparison between the results of VIM solutions and exact solution is given. The fractional derivatives are described in Caputo sense.

scholarly journals New analytical solution for natural convection of Darcian fluid in porous media prescribed surface heat flux

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 221-227 ◽  
Author(s):  
Domiry Ganji ◽  
Hasan Sajjadi
Keyword(s):  
Heat Flux ◽  
Porous Media ◽  
Differential Equations ◽  
Iteration Method ◽  
Surface Heat Flux ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Surface Heat ◽  
Variational Iteration ◽  
He’S Variational Iteration Method

A new analytical method called He's Variational Iteration Method is introduced to be applied to solve nonlinear equations. In this method, general Lagrange multipliers are introduced to construct correction functional for the problems. It is strongly and simply capable of solving a large class of linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term and also is very user friend because it reduces the size of calculations besides; its iterations are direct and straightforward. In this paper the powerful method called Variational Iteration Method is used to obtain the solution for a nonlinear Ordinary Differential Equations that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. The obtained Variational Iteration Method solution in comparison with the numerical ones represents a remarkable accuracy.

scholarly journals Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Fukang Yin ◽  
Junqiang Song ◽  
Hongze Leng ◽  
Fengshun Lu
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Operational Matrix ◽  
Variational Iteration Method ◽  
Legendre Functions ◽  
Variational Iteration ◽  
Fractional Differential

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique.

scholarly journals Solution of Space-Time-Fractional Problem by Shehu Variational Iteration Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Suleyman Cetinkaya ◽  
Ali Demir ◽  
Hulya Kodal Sevindir
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Space Time ◽  
Variational Iteration ◽  
Mathematical Problems ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

In this study, we deal with the problem of constructing semianalytical solution of mathematical problems including space-time-fractional linear and nonlinear differential equations. The method, called Shehu Variational Iteration Method (SVIM), applied in this study is a combination of Shehu transform (ST) and variational iteration method (VIM). First, ST is utilized to reduce the time-fractional differential equation with fractional derivative in Liouville-Caputo sense into an integer-order differential equation. Later, VIM is implemented to construct the solution of reduced differential equation. The convergence analysis of this method and illustrated examples confirm that the proposed method is one of best procedures to tackle space-time-fractional differential equations.

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