Exponential Spline Method for Solving Fuzzy Integro-Differential Equations

Abstract

In this paper, we consider a new class of fuzzy functions called Fuzzy Integro-Differential Equations.Some numerical methods, such as cubic spline have been used to determine the solutions of these equations. We extend these numerical techniques to find the optimal solutions. Exponential spline technique is used for this. The results shown that Exponential spline method is more accurate in terms of absolute error. Based on the parametric form of the fuzzy number, the integro-differential equation is contacted into two systems of the second kind. Illustrative examples are given to demonstrate the high precision and good performance of the new class. Graphical representations reveal the symmetry between lower and upper cut represent of fuzzy solutions and may be helpful for a better understanding of fuzzy model artificial, intelligence, medical science and quantum.