Numerical simulation of fuzzy differential equations using general linear method and B-series

Abstract

In this article, numerical simulation of fuzzy differential equations using general linear method is proposed. The significance of general linear method is derivation of algebraic order conditions of method using technique of rooted trees and B-series. Fuzzy general linear method of order 3 based on the concept of generalized Hukuhara differentiability for solving fuzzy differential equations is developed. Convergence of third-order fuzzy general linear method is proven. The proposed method is tested on fuzzy initial value problems, and the numerical results showed that fuzzy general linear method produced more accurate approximation of fuzzy solution for tested problems compared with the existing fuzzy numerical methods.