Solution to first-order fuzzy differential equation using numerical methods

Abstract

In day-to-day life, we face uncertainty due to a lack of knowledge and accurate information about the mathematical model, so it is critical to understand the model’s behavior. There are many techniques to solve mathematical models; in that case, to deal with the dynamic mathematical model, a differential equation is the best fitting tool. The fuzzy environment allows identifying the behavior of an uncertain dynamic mathematical model. Hence, in this chapter, the solution to fuzzy differential equation using numerical methods and its generalization in fuzzy and intuitionistic environments is discussed. There are different numerical methods; among them, the two best methods, namely Euler’s and modified Euler’s methods, are used to solve first-order ordinary differential equations in the two different environments. Furthermore, the tables show solutions at different α-cut and (α, β)-cut values with varying time by tabular data.