Using finite difference method for solving linear two-point fuzzy boundary value problems based on extension principle

Subject Areas : Applied Mathematics

Seyed Majid  Alavi ¹ (Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran)

Received: 2020-02-10 Accepted : 2020-06-17 Published : 2020-12-01

Keywords: Zadeh's extension Principle, Finite difference, fuzzy number, fuzzy differential equation, Fuzzy boundary value problems,

Abstract :

In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matrix. This linear system determines $r$-level of fuzzy solution at mesh points. By combining of this solutions, we obtain fuzzy solution of main problem at mesh points, approximately. Its applicabilityis illustrated by someexamples