Approximated solution of First order Fuzzy Differential Equations under generalized differentiability

Subject Areas : Statistics

T. Allahviranloo ¹ ( Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran )
N. Ahmady ² ( Department of Mathematics, Varamin-Pishva Branch, Islamic Azad University, Varamin, Iran )
E. Ahmady ³ ( Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran )

Received: 2017-02-28 Accepted : 2017-04-19 Published : 2017-02-01

Keywords: معادلات دیفرانسیل فازی, مشتق هاکوهارا تعمیم یافته, روش عددی,

Abstract :

In this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations. The existence, uniqueness and convergence of the approximate solution are investigated. To show the advantage of method, this method is compared with the Euler method that was introduced in [۱], and it is shown this method is more accurate than Euler method for solving fuzzy differential equations under generalized differentiability.