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 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 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 Variational Iteration Method for Analytical Solution of the Lane-Emden Type Equation with Singular Initial and Boundary Conditions

2019 ◽  
pp. 127-142 ◽  
Author(s):  
Muhammad Nadeem ◽  
Hijaz Ahmad
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Type Equation ◽  
Variational Iteration Method ◽  
Mathematical Physics ◽  
Initial Value ◽  
Emden Equation ◽  
Variational Iteration

In this paper, a well-known equation used in astrophysics and mathematical physics called the Lane-Emden equation is to be solved by a variational iteration method. The main purpose of this approach is to solve the singular initial value problems and also boundary value problem of Lane-Emden type equations. This technique overcomes its singularity at origin rapidly. It gives the approximate and exact solution with easily computable terms. The approach is illustrated with some examples to show its reliability and compactness.

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 Variational Iteration Method for Singular Perturbation Initial Value Problems with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yongxiang Zhao ◽  
Aiguo Xiao ◽  
Li Li ◽  
Chengjian Zhang
Keyword(s):  
Singular Perturbation ◽  
Lagrange Multipliers ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Variational Iteration Method ◽  
Variational Theory ◽  
Initial Value ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Convergence Results

The variational iteration method (VIM) is applied to solve singular perturbation initial value problems with delays (SPIVPDs). Some convergence results of VIM for solving SPIVPDs are given. The obtained sequence of iterates is based on the use of general Lagrange multipliers; the multipliers in the functionals can be identified by the variational theory. Moreover, the numerical examples show the efficiency of the method.

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