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

Abstract

The 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.

Solutions of fractional differential equations by Sumudu transform and variational iteration method

“…This technique was developed into a powerful analytical method, (Variational iteration method -VIM) [12] for solving differential equations. The method was applied to initial boundary value problems [1,13,26,36,37] and fuzzy equations [17,18,30], etc. Generally, in solving initial value problems of differential equations by VIM, the crucial point is identifying the Lagrange multipliers.…”

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

“…It can be concluded that the crucial step of the method is to identify the Lagrange multipliers in a more accurate way. In view of this point, several modified versions and new applications were suggested recently, see for example [22][23][24][25][26][27]. Consider the following often used FDE to illustrate the basic idea of the method,…”

A Hybrid Modified Approach for Solving Fuzzy Differential Equations

“…While the variational iteration method (VIM) was developed by He [10,11] for solving nonlinear problems, it has been successful applied on initial and boundary value problems. The fuzzy variational iteration method (FVIM) has been applied by Jafari [12] to finding solutions of nth order linear fuzzy differential equations. The solution obtained by the variational iteration method was an infinite power series, which, with appropriate initial condition, can be expressed in a closed form, i.e.…”