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

Abstract

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.

Using Variational Iteration Method for Solving Linear Fuzzy Random Ordinary Differential Equations

“…where, L is a linear operator, N is a nonlinear operator [7], g is a known analytical function. The approximate solution by using the VIM will be in the form as in the following correction functional:…”

“…Allahvivallcoo et al [5] in 2014 and Sadigh Behzadi et al [6] in 2018 also used the VIM to solve nonlinear FODEs and the 2nd-order Abel-Volterra fuzzy integro-differential equation, respectively. In 2021, Fadhel and Sagban enhanced the VIM to yield more precise results and expedite the convergence of the approximate numerical solution towards the exact solution [7].…”

Variational Iteration Approach for Solving Two-Points Fuzzy Boundary Value Problems

“…Mahdi S.R (reference [15]) and Sagban H.M (reference [11]) introduced the solution of fuzzy ODEs with initial conditions using the well-known VIM. In this section, the second order two-point fuzzy BVPs will be solved using the VIM.…”

“…Hussein M. Sagban in 2021 studied the solution of fuzzy initial value problem, using the modified variational iteration method (VIM), in which the fuzziness occurs in the initial conditions [11]. Rasheed in 2022 presented an approximate method for solving fuzzy differential and integral equations.…”