scholarly journals Modified variational iteration method for straight fins with temperature dependent thermal conductivity

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 229-236 ◽  
Author(s):  
Mustafa Inc ◽  
Hasib Khan ◽  
Dumitru Baleanu ◽  
Aziz Khan
Keyword(s):  
Thermal Conductivity ◽  
Iteration Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Temperature Dependent ◽  
Convergence Region ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Temperature Dependent Thermal Conductivity ◽  
Modified Variational Iteration Method

The modified variational iteration method (MVIM) has been used to calculate the efficiency of straight fins with temperature dependent thermal conductivity. The obtained results are compared with homotopy analysis method (HAM), homotopy perturbation method (HPM), and Adomian decomposition method (ADM). It is used w ? 0 auxiliary parameter to keep under control convergence region of solution series in MVIM. As a result, although MVIM and HAM give results close to each other; HPM and ADM give divergent results from analytical solution.

scholarly journals Analysis of Convective Straight and Radial Fins with Temperature-Dependent Thermal Conductivity Using Variational Iteration Method with Comparison with Respect to Finite Element Analysis

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Safa Bozkurt Coşkun ◽  
Mehmet Tarik Atay
Keyword(s):  
Thermal Conductivity ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Large Temperature ◽  
Temperature Dependent ◽  
Element Analysis ◽  
Variational Iteration ◽  
Temperature Dependent Thermal Conductivity

In order to enhance heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilized. Especially in the case of large temperature differences, variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze convective straight and radial fins with temperature-dependent thermal conductivity. In order to show the efficiency of variational iteration method (VIM), the results obtained from VIM analysis are compared with previously obtained results using Adomian decomposition method (ADM) and the results from finite element analysis. VIM produces analytical expressions for the solution of nonlinear differential equations. However, these expressions obtained from VIM must be tested with respect to the results obtained from a reliable numerical method or analytical solution. This work assures that VIM is a promising method for the analysis of convective straight and radial fin problems.

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.

A NEWLY MODIFIED VARIATIONAL ITERATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350029
Author(s):  
R. YULITA MOLLIQ ◽  
M. S. M. NOORANI
Keyword(s):  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Method Comparison ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Accurate Method ◽  
Convergence Region ◽  
Variational Iteration ◽  
Approximate Analytical Solutions ◽  
Modified Variational Iteration Method

This paper presents a new reliable modification of the variational iteration method (MoVIM). An enlarged interval of convergence region of series solutions is obtained by inserting a nonzero auxiliary parameter (ℏ) into the correction functional of variational iteration method. Approximate analytical solutions for some examples of nonlinear problems are obtained using variational iteration method. Comparison with the exact solution, Runge–Kutta method 4, and also another modified variational iteration method has shown that MoVIM is an accurate method for solving nonlinear problems.

scholarly journals VIM for Solving the Pollution Problem of a System of Lakes

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
J. Biazar ◽  
M. Shahbala ◽  
H. Ebrahimi
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Environment Monitoring ◽  
System Of Differential Equations ◽  
Variational Iteration ◽  
Pollution Problem ◽  
Adomian Decomposition ◽  
Different Types

Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. The use of differential equations of monitoring pollution has become possible. In this paper the pollution problem of three lakes with interconnecting channels has been studied. The variational iteration method has been applied to compute an approximate solution of the system of differential equations, governing on the problem. Three different types of input models: sinusoidal, impulse, and step will be considered for monitoring the pollution in the lakes. The results are compared with those obtained by Adomian decomposition method. This comparison reveals that the variational iteration method is easier to be implemented.

scholarly journals Numerical Simulation of the FitzHugh-Nagumo Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. A. Soliman
Keyword(s):  
Numerical Simulation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Nagumo Equations

The variational iteration method and Adomian decomposition method are applied to solve the FitzHugh-Nagumo (FN) equations. The two algorithms are illustrated by studying an initial value problem. The obtained results show that only few terms are required to deduce approximated solutions which are found to be accurate and efficient.

scholarly journals A New Reconstruction of Variational Iteration Method and Its Application to Nonlinear Volterra Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
K. Maleknejad ◽  
M. Tamamgar
Keyword(s):  
Exact Solution ◽  
Iteration Method ◽  
Decomposition Method ◽  
Solution Process ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Adomian Decomposition

We reconstruct the variational iteration method that we call, parametric iteration method (PIM). The purposed method was applied for solving nonlinear Volterra integrodifferential equations (NVIDEs). The solution process is illustrated by some examples. Comparisons are made between PIM and Adomian decomposition method (ADM). Also exact solution of the 3rd example is obtained. The results show the simplicity and efficiency of PIM. Also, the convergence of this method is studied in this work.

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