scholarly journals Modified variational iteration method (non-homogeneous initial value problem)

2012 ◽  
Vol 55 (3-4) ◽  
pp. 1222-1232
Author(s):  
Tamer A. Abassy
Keyword(s):  
Initial Value Problem ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

scholarly journals Approximate Solution of Linear Fuzzy Initial Value Problems Using Modified Variaional Iteration Method

2021 ◽  
Vol 24 (4) ◽  
pp. 32-39
Author(s):  
Hussein M. Sagban ◽  
◽  
Fadhel S. Fadhel ◽  
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

The main objective of this paper is to solve fuzzy initial value problems, in which the fuzziness occurs in the initial conditions. The proposed approach, namely the modified variational iteration method, will be used to find the solution of fuzzy initial value problem approximately and to increase the rate of convergence of the variational iteration method. From the obtained results, as it is expected, the approximate results of the proposed method are more accurate than those results obtained without using the modified variational iteration method.

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 Modified variational iteration method for variant Boussinesq equation

2015 ◽  
Vol 19 (4) ◽  
pp. 1195-1199 ◽  
Author(s):  
Jun-Feng Lu
Keyword(s):  
Exact Solutions ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Boussinesq Equation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

In this paper, we solve the variant Boussinesq equation by the modified variational iteration method. The approximate solutions to the initial value problems of the variant Boussinesq equation are provided, and compared with the exact solutions. Numerical experiments show that the modified variational iteration method is efficient for solving the variant Boussinesq equation.

scholarly journals Approximate Solutions for Nonlinear Initial Value Problems Using the Modified Variational Iteration Method

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Taher A. Nofal
Keyword(s):  
Iteration Method ◽  
Initial Value Problems ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Short Wave ◽  
Systems Of Nonlinear Equations ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

We have used the modified variational iteration method (MVIM) to find the approximate solutions for some nonlinear initial value problems in the mathematical physics, via the Burgers-Fisher equation, the Kuramoto-Sivashinsky equation, the coupled Schrodinger-KdV equations, and the long-short wave resonance equations together with initial conditions. The results of these problems reveal that the modified variational iteration method is very powerful, effective, convenient, and quite accurate to systems of nonlinear equations. It is predicted that this method can be found widely applicable in engineering and physics.

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.

scholarly journals Variational iteration method for the classical Drinfel’d-Sokolov-Wilson equation

2014 ◽  
Vol 18 (5) ◽  
pp. 1543-1546 ◽  
Author(s):  
Lin Jin ◽  
Jun-Feng Lu
Keyword(s):  
Initial Value Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Variational Iteration Method ◽  
Wilson Equation ◽  
Initial Value ◽  
Variational Iteration

In this paper, we apply the variational iteration method to solve the classical Drinfel?d-Sokolov-Wilson equation. The initial value problem of the classical Drinfel?d-Sokolov-Wilson equation is considered. Numerical experiments are presented to show the efficiency of the method.

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.

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