scholarly journals On linear and nonlinear fractional PDEs

2013 ◽  
Vol 40 (4) ◽  
pp. 511-524
Author(s):  
Jamshad Ahmad ◽  
Hassany ul ◽  
Syed Mohyud-Din
Keyword(s):  
Exact Solution ◽  
Fractional Derivative ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Nonlinear Partial Differential Equations ◽  
Variational Iteration Method ◽  
High Accuracy ◽  
New Approach ◽  
Fractional Pdes ◽  
Linear And Nonlinear

In this study, Variational Iteration Method (VIM) has been applied to obtain the analytical solutions of fractional order nonlinear partial differential equations. The iteration procedure is based on a relatively new approach which is called Jumarie?s fractional derivative. Several examples have been solved to elucidate effectiveness of the proposed method and the results are compared with the exact solution, revealing high accuracy and efficiency of the method.

The Variational IterationMethod for Finding Exact Solution of Nonlinear Gas Dynamics Equations

2011 ◽  
Vol 66 (3-4) ◽  
pp. 161-164 ◽  
Author(s):  
Hossein Jafari ◽  
Ch. Chun ◽  
C.M. Khalique
Keyword(s):  
Exact Solution ◽  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Iteration Method ◽  
Gas Dynamics ◽  
Variational Iteration Method ◽  
Gas Dynamics Equations ◽  
Exact Analytical Solutions ◽  
Gas Dynamics Equation

The variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method to solve nonlinear equations. In this paper, a modified VIM is introduced to accelerate the convergence of VIM and it is applied for finding exact analytical solutions of nonlinear gas dynamics equation.

scholarly journals Study of the Nonlinear Dropping Shock Response of Expanded Foam Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Huan-xin Jiang ◽  
Yong Zhu ◽  
Li-xin Lu
Keyword(s):  
Numerical Simulation ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Equation Of Motion ◽  
High Accuracy ◽  
Packaging System ◽  
First Order ◽  
Approximate Analytical Solutions ◽  
Shock Response

The variational iteration method-2 (VIM-2) is applied to obtain approximate analytical solutions of EPS foam cushioning packaging system. The first-order frequency solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm. The results showed the high accuracy of this VIM with convenient calculation.

scholarly journals Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem

2013 ◽  
Vol 17 (3) ◽  
pp. 715-721 ◽  
Author(s):  
Chun-Feng Liu ◽  
Shan-Shan Kong ◽  
Shu-Juan Yuan
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Variational Iteration Method ◽  
High Accuracy ◽  
Variational Iteration

A reconstructive scheme for variational iteration method using the Yang-Laplace transform is proposed and developed with the Yang-Laplace transform. The identification of fractal Lagrange multiplier is investigated by the Yang-Laplace transform. The method is exemplified by a fractal heat conduction equation with local fractional derivative. The results developed are valid for a compact solution domain with high accuracy.

scholarly journals The variational iteration method for solving n-th order fuzzy differential equations

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Mohammad Saeidy ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Analytical Method ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Linear Differential Equations ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.

Variational Iteration Method for a Nonlinear Reaction-Diffusion Process

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Shu-Qiang Wang ◽  
Ji-Huan He
Keyword(s):  
Exact Solution ◽  
Diffusion Process ◽  
Iteration Method ◽  
Unknown Parameter ◽  
Reaction Diffusion ◽  
Variational Iteration Method ◽  
Rigorous Derivation ◽  
Variational Iteration ◽  
Nonlinear Reaction ◽  
The Given

An extremely simple and elementary, but rigorous derivation of temperature distribution of a reaction-diffusion process is given using the variational iteration method. In this method, a trial function (an initial solution) is chosen with some unknown parameter, which is identified after a few iterations according to the given boundary conditions. Comparison with the exact solution shows that the method is very effective and convenient.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Adel Al-Rabtah ◽  
Shaher Momani ◽  
Mohamed A. Ramadan
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Spline Functions ◽  
Exact Analytical Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Good Agreement

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for0<α≤1andα≥1, whereαdenotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented elsewhere. Results also show that the technique introduced here is robust and easy to apply.

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