scholarly journals A dye removal model with a fuzzy initial condition

2016 ◽  
Vol 20 (3) ◽  
pp. 867-870 ◽  
Author(s):  
Yan Zhang ◽  
Ji-Huan He ◽  
Shu-Qiang Wang ◽  
Ping Wang
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Textile Industry ◽  
Dye Removal ◽  
Transport Model ◽  
Fuzzy Model ◽  
Variational Iteration Method ◽  
Initial Condition ◽  
Removal Model ◽  
Industry Wastewater

A fuzzy model for dye removal is suggested to study a transport model of the direct textile industry wastewater, and the variational iteration method is adopted to obtain its analytical solutions. The concentration depends upon not only the parameters in the governing equation, but also the pair of the initial condition.

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.

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 Analytical solutions of time-fractional advection problem

2016 ◽  
Vol 12 (6) ◽  
pp. 6286-6289
Author(s):  
Huimin Wang
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
The Other ◽  
Variational Iteration

we use variational iteration method (VIM) to solve some nonlinear time-fractional advection problem.Compared to the other method, the VIM is direct and straightforward.

scholarly journals Determining An Unknown Boundary Condition by An Iteration Method

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 409
Author(s):  
Dejian Huang ◽  
Yanqing Li ◽  
Donghe Pei
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Heat Conduction ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Variational Iteration Method ◽  
Conduction Equation ◽  
Unknown Boundary ◽  
Initial Condition

This paper investigates the boundary value in the heat conduction problem by a variational iteration method. Applying the iteration method, a sequence of convergent functions is constructed, the limit approximates the exact solution of the heat conduction equation in a few iterations using only the initial condition. This method does not require discretization of the variables. Numerical results show that this method is quite simple and straightforward for models that are currently under research.

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 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.

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