Variational iteration method for Hirota‐Satsuma coupled KdV equation using auxiliary parameter

2012 ◽  
Vol 22 (3) ◽  
pp. 277-286 ◽  
Author(s):  
Said Mohammad Mehdi Hosseini ◽  
Syed Tauseef Mohyud‐Din ◽  
Husain Ghaneai
Keyword(s):  
Iteration Method ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Auxiliary Parameter ◽  
Variational Iteration ◽  
Coupled Kdv Equation

scholarly journals An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Hakeem Ullah ◽  
Saeed Islam ◽  
Muhammad Idrees ◽  
Mehreen Fiza ◽  
Zahoor Ul Haq
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Asymptotic Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Optimal Homotopy Asymptotic Method

We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM). We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM) and homotopy perturbation method (HPM) solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

scholarly journals Variational Iteration Method for Nonlinear Age-Structured Population Models Using Auxiliary Parameter

2010 ◽  
Vol 65 (12) ◽  
pp. 1137-1142 ◽  
Author(s):  
Said Muhammad Mehdi Hosseini ◽  
Syed Tauseef Mohyud-Din ◽  
Hussain Ghaneai
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Population Models ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Structured Population Models ◽  
Variational Iteration ◽  
Structured Population ◽  
Age Structured ◽  
Age Structured Population

In this paper, we apply He’s variational iteration method (VIM) coupled with an auxiliary parameter which proves very effective to control the convergence region of an approximate solution. Moreover, a convenient way is considered for choosing a suitable auxiliary parameter via a residual function. The proposed algorithm is tested on some nonlinear age-structured population models, and numerical results explicitly reveal the complete reliability, efficiency, and accuracy of the suggested technique. It is observed that the approach may be implemented on other nonlinear models of physical nature.

scholarly journals Analytical approach to a generalized Hirota-Satsuma coupled Korteweg-de Vries equation by modified variational iteration method

2016 ◽  
Vol 20 (3) ◽  
pp. 885-888 ◽  
Author(s):  
Jun-Feng Lu ◽  
Li Ma
Keyword(s):  
Iteration Method ◽  
Analytical Approach ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
De Vries ◽  
Modified Variational Iteration Method

In this paper, we apply the modified variational iteration method to a generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation. The numerical solutions of the initial value problem of the generalized Hirota-Satsuma coupled KdV equation are provided. Numerical results are given to show the efficiency of the modified variational iteration method.

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