Numerical Solution of Fuzzy Differential Equations Based on Taylor Series by Using Fuzzy Neural Networks

Mazin H.Suhhiem; Eman A.Hussian; Eman A.Hussian; Eman A.Hussian

doi:10.24297/jam.v11i3.1267

Authors

Mazin H.Suhhiem Dep. of statistics, College of Adm. and Econ., University of sumar, Alrefiey,Iraq.
Eman A.Hussian College of Sciences,AL-Mustansiriyah University,Baghdad,Iraq
Eman A.Hussian College of Sciences,AL-Mustansiriyah University,Baghdad,Iraq
Eman A.Hussian College of Sciences,AL-Mustansiriyah University,Baghdad,Iraq

DOI:

https://doi.org/10.24297/jam.v11i3.1267

Keywords:

Fuzzy differential equation, Fuzzy neural network, Feed-forward neural network, BFGS method, Hyperbolic tangent function .

Abstract

In this paper a new method based on learning algorithm of Fuzzy neural network and Taylor series has been developed for obtaining numerical solution of fuzzy differential equations.A fuzzy trial solution of the fuzzy initial value problem is written as a sum of two parts.The first part satisfies the fuzzy initial condition,it contains Taylor series and involves no fuzzy adjustable parameters.The second part involves a feed-forward fuzzy neural network containing fuzzy adjustable parameters (the fuzzy weights).Hence by construction,the fuzzy initial condition is satisfied and the fuzzy network is trained to satisfy the fuzzy differential equation . In comparison with existing similar neural networks,the proposed method provides solutions with high accuracy.Finally , we illustrate our approach by two numerical examples .