Development of Basic Science Variational Iteration Method for n-th Order Fuzzy Differential Equations: Theoretical Framework and Convergence Analysis

This paper presents a theoretical framework for applying the Variational Iteration Method (VIM) to solve n-th order fuzzy differential equations. By transforming higher-order fuzzy differential equations into systems of first-order fuzzy differential equations, the VIM formulation can be systematically extended to arbitrary-order problems. The method is developed using the parametric representation of fuzzy numbers and the Seikkala derivative. A convergence analysis is provided in the Hausdorff metric under suitable Lipschitz conditions on the nonlinear term. The theoretical results demonstrate that the iterative sequence generated by the VIM converges to the exact fuzzy solution. A numerical example illustrates the effectiveness and rapid convergence of the proposed approach.

کلیدواژه ها:

Fuzzy differential equations ، Variational iteration method ، Convergence analysis ، Seikkala derivative ، Hausdorff metric