Numerical Approach 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 Euler, have been used to determine the solutions of these equations. We extend these numerical techniques to find the optimal solutions by using control parameters, the extended difference Euler technique is used for this. Based on the parametric form of the fuzzy number, the Integro- Differential Equation is divided 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 models in artificial intelligence and medical science. The results show that the extended Euler method is more accurate in terms of absolute error.

Keywords

• Fuzzy integro-differential equations, extended difference Euler method, Exact solution, Approximate solution, fuzzy parameter, control parameters