Numerical Solution of Fuzzy Partial Differential Equations by Using Modified Fuzzy Neural Networks

The aim of this work is to present a modified method for finding the numerical solutions of fuzzy partial differential equations by using fuzzy artificial neural networks. Using a fuzzy trial neural solution depending on the fuzzy initial values ​​and the fuzzy boundary conditions of the problem. Using modified fuzzy neural network makes that training points should be selected over an open interval without training the network in the range of first and end points. In fact, This new method based on replacing each element in the training set by a polynomial of first degree. The fuzzy trial solution of fuzzy partial differential equation is written as a sum of two parts. The first part satisfies the fuzzy conditions, it contains no fuzzy adjustable parameters. The second part involves a feed-forward fuzzy neural network containing fuzzy adjustable parameters. In comparison with existing similar fuzzy neural networks, the proposed method provides solutions with high accuracy. Finally, we illustrate our approach by two problems.