scholarly journals Exact solution of the heat equation with boundary condition of the fourth kind by He’s variational iteration method

2009 ◽  
Vol 58 (11-12) ◽  
pp. 2495-2503 ◽  
Author(s):  
Damian Słota
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Heat Equation ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Fourth Kind

scholarly journals He's Variational Iteration Method for Solving Fractional Riccati Differential Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
H. Jafari ◽  
H. Tajadodi
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Iteration Method ◽  
Present Method ◽  
Variational Iteration Method ◽  
Riccati Differential Equation ◽  
Variational Iteration ◽  
Optimal Value ◽  
He’S Variational Iteration Method ◽  
Sequence Of Functions

We will consider He's variational iteration method for solving fractional Riccati differential equation. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converges to the exact solution of the problem. The present method performs extremely well in terms of efficiency and simplicity.

scholarly journals Application of He’s Variational Iteration Method to Nonlinear Integro-Differential Equations

2010 ◽  
Vol 65 (5) ◽  
pp. 418-430 ◽  
Author(s):  
Ahmet Yildirim
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Mathematical Tool ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

In this paper, an application of He’s variational iteration method is applied to solve nonlinear integro-differential equations. Some examples are given to illustrate the effectiveness of the method. The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations

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.

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