Beyond Adomian method: The variational iteration method for solving heat-like and wave-like equations with variable coefficients

2008 ◽  
Vol 372 (3) ◽  
pp. 233-237 ◽  
Author(s):  
Da-Hua Shou ◽  
Ji-Huan He
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Variational Iteration ◽  
Adomian Method

scholarly journals A General Iteration Formula of VIM for Fractional Heat- and Wave-Like Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Fukang Yin ◽  
Junqiang Song ◽  
Xiaoqun Cao
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Iteration Formula ◽  
Variational Iteration

A general iteration formula of variational iteration method (VIM) for fractional heat- and wave-like equations with variable coefficients is derived. Compared with previous work, the Lagrange multiplier of the method is identified in a more accurate way by employing Laplace’s transform of fractional order. The fractional derivative is considered in Jumarie’s sense. The results are more accurate than those obtained by classical VIM and the same as ADM. It is shown that the proposed iteration formula is efficient and simple.

The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Porous Medium ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Scientific Models ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
Variational Iteration ◽  
Hybrid Selection ◽  
Linear And Nonlinear

AbstractWe apply the variational iteration method (VIM) for solving linear and nonlinear ordinary differential equations with variable coefficients. We use distinct Lagrange multiplier for each order of ODE. We emphasize the power of the method by testing a variety of models with distinct orders and variable coefficients. Scientific models, namely, the hybrid selection model, the Thomas-Fermi equation, the Kidder equation of the Unsteady flow of gas through a porous medium, and the Riccati equation, are studied as well.

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