scholarly journals Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li Chen ◽  
Yang Zhao ◽  
Hossein Jafari ◽  
J. A. Tenreiro Machado ◽  
Xiao-Jun Yang
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Mathematical Physics ◽  
Nondifferentiable Functions ◽  
Independent Variables ◽  
Poisson Equations ◽  
Variational Iteration ◽  
Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

scholarly journals Local Fractional Laplace Variational Iteration Method for Nonhomogeneous Heat Equations Arising in Fractal Heat Flow

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Shu Xu ◽  
Xiang Ling ◽  
Carlo Cattani ◽  
Gong-Nan Xie ◽  
Xiao-Jun Yang ◽  
...  
Keyword(s):  
Heat Flow ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Previous Method ◽  
Heat Equations ◽  
Nondifferentiable Functions ◽  
Variational Iteration ◽  
Nonhomogeneous Heat

The local fractional Laplace variational iteration method is used for solving the nonhomogeneous heat equations arising in the fractal heat flow. The approximate solutions are nondifferentiable functions and their plots are also given to show the accuracy and efficiency to implement the previous method.

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 Approximate Solutions for Local Fractional Linear Transport Equations Arising in Fractal Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Meng Li ◽  
Xiao-Feng Hui ◽  
Carlo Cattani ◽  
Xiao-Jun Yang ◽  
Yang Zhao
Keyword(s):  
Porous Media ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Transport Equations ◽  
Nondifferentiable Functions ◽  
Linear Transport ◽  
Variational Iteration

We investigate the local fractional linear transport equations arising in fractal porous media by using the local fractional variational iteration method. Their approximate solutions within the nondifferentiable functions are obtained and their graphs are also shown.

scholarly journals Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
C. Ünlü ◽  
H. Jafari ◽  
D. Baleanu
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Initial Position ◽  
Fractional Order Differential Equations ◽  
Variational Iteration ◽  
Fractional Differential

A modification of the variational iteration method (VIM) for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE) obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.

scholarly journals Variational iteration method for studying perihelion precession and deflection of light in General Relativity

2016 ◽  
Vol 4 (2) ◽  
pp. 52 ◽  
Author(s):  
V.K. Shchigolev
Keyword(s):  
General Relativity ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Simple Problem ◽  
Geodesic Equations ◽  
Variational Iteration ◽  
Deflection Of Light ◽  
Perihelion Shift ◽  
Main Ideas

A new approach in studying the planetary orbits and deflection of light in General Relativity (GR) by means of the Variational iteration method (VIM) is proposed in this paper. For this purpose, a brief review of the nonlinear geodesic equations in the spherical symmetry spacetime and the main ideas of VIM are given. The appropriate correct functionals are constructed for the geodesics in the spacetime of Schwarzschild, Reissner-Nordström and Kiselev black holes. In these cases, the Lagrange multiplier is obtained from the stationary conditions for the correct functionals. Then, VIM leads to the simple problem of computation of the integrals in order to obtain the approximate solutions of the geodesic equations. On the basis of these approximate solutions, the perihelion shift and the light deflection have been obtained for the metrics mentioned above.

A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Hale Tajadodi ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equation ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Convergence Region ◽  
Riccati Differential Equation ◽  
Adomian Polynomials ◽  
Riccati Differential Equations ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

AbstractIn this paper, we introduce a modified variational iteration method (MVIM) for solving Riccati differential equations. Also the fractional Riccati differential equation is solved by variational iteration method with considering Adomians polynomials for nonlinear terms. The main advantage of the MVIM is that it can enlarge the convergence region of iterative approximate solutions. Hence, the solutions obtained using the MVIM give good approximations for a larger interval. The numerical results show that the method is simple and effective.

scholarly journals Variational Iteration Method for a Fractional-Order Brusselator System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Jafari ◽  
Abdelouahab Kadem ◽  
D. Baleanu
Keyword(s):  
Fractional Order ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Promising Tool ◽  
Approximate Analytical Solutions ◽  
Fractional Differential ◽  
Linear And Nonlinear

This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.

scholarly journals Variational Iteration Method for Volterra Functional Integrodifferential Equations with Vanishing Linear Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Konuralp ◽  
H. Hilmi Sorkun
Keyword(s):  
Exact Solutions ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Test Problems ◽  
Application Process ◽  
Delay Function ◽  
Variational Iteration

Application process of variational iteration method is presented in order to solve the Volterra functional integrodifferential equations which have multi terms and vanishing delays where the delay functionθ(t)vanishes inside the integral limits such thatθ(t)=qtfor0<q<1,t≥0. Either the approximate solutions that are converging to the exact solutions or the exact solutions of three test problems are obtained by using this presented process. The numerical solutions and the absolute errors are shown in figures and tables.

scholarly journals A variational iteration method integral transform technique for handling heat transfer problems

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 55-61 ◽  
Author(s):  
Yuejin Zhou ◽  
Shun Pang ◽  
Guo Chong ◽  
Xiaojun Yang ◽  
Xiaoding Xu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Iteration Method ◽  
Integral Transform ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Excess Temperature ◽  
Variational Iteration ◽  
Transfer Equations ◽  
Transfer Problems ◽  
Integral Transform Technique

In this paper, we consider the heat transfer equations at the low excess temperature. The variational iteration method integral transform technique is used to find the approximate solutions for the problems. The used method is accurate and efficient.

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