scholarly journals A Hybrid Modified Approach for Solving Fuzzy Differential Equations

2017 ◽  
Vol 5 (2) ◽  
Author(s):  
Alauldeen N. Ahmad ◽  
Basma A. Nema
Keyword(s):  
Differential Equations ◽  
Lagrange Multiplier ◽  
Hybrid Method ◽  
Iteration Method ◽  
Laplace Transformation ◽  
Variational Iteration Method ◽  
Ranking Method ◽  
Lower Upper ◽  
Variational Iteration ◽  
Fuzzy Parameters

In this paper, a hybrid method is presented by combining Laplace transformation and variational iteration method for solving fuzzy differential equations with fuzzy initial and boundaries values. A defuzzification technique had been implemented to convert the fuzzy parameters into crisp values by building an extended ranking method. Then the method is implemented on the new problem in which two approaches has been built according to the formula of  Lagrange multiplier obtaining the lower, upper and center solutions.

Solve fractional differential equations via a hybrid method between variational iteration method and gray wolf optimization algorithm

2020 ◽  
pp. 2150144
Author(s):  
Ahmed Entesar ◽  
Omar Saber Qasim
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Hybrid Method ◽  
Optimization Algorithm ◽  
Iteration Method ◽  
Optimal Parameter ◽  
Variational Iteration Method ◽  
Gray Wolf ◽  
Variational Iteration ◽  
Fractional Differential

In this paper, a hybrid method between Variational Iteration Method (VIM) and gray wolf optimization algorithm (GWO) was proposed to solve the fractional differential equations (FDE), where the optimal parameter value ([Formula: see text] for the VIM was estimated by the GWO. The solutions in the proposed method, GWO-VIM, demonstrated the efficiency and reliability compared to the default method VIM, by calculating the maximum absolute errors (MAE) and mean square error (MSE).

scholarly journals On the Computation of the Lagrange Multiplier for the Variational Iteration Method (VIM) for Solving Differential Equations

2020 ◽  
pp. 74-92
Author(s):  
N. Okiotor ◽  
F. Ogunfiditimi ◽  
M. O. Durojaye
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Integrating Factor ◽  
Variational Iteration ◽  
Approximate Result ◽  
Number Of Iterations

In this study, the Variational Iteration Method (VIM) is applied in finding the solution of differential equations with emphasis laid on the choice of the Lagrange multiplier used while employing VIM. Building on existing methods and variational theories, the operator D-Method and integrating factor are employed in certain aspects in the determination of exact Lagrange multiplier for VIM. When results of the computed exact Lagrange multiplier were compared with results of approximate Lagrange multiplier, it was observed that the computed exact Lagrange multiplier reduced significantly the number of iterations required to get a good approximate result, and in some cases the result converged to the exact solution after a single iteration. Evaluations are carried out using MAPLE Software.

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

scholarly journals The variational iteration method for solving n-th order fuzzy differential equations

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Mohammad Saeidy ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Analytical Method ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Linear Differential Equations ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.

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