Numerical Solution for Fuzzy Initial Value Problems via Interactive Arithmetic: Application to Chemical Reactions

Abstract

This paper studies numerical solutions for fuzzy initial value problems, where the initial conditions are given by interactive fuzzy numbers. The fuzzy solution is given by a numerical method that employs the arithmetic of interactive fuzzy numbers and yields a fuzzy number at each instant of time. The computational cost of the numerical method is also provided. The chemical decay reaction model is considered in order to illustrate that different types of interactivity produce different solutions for initial value problems. In addition, we present an application to the Lotka–Volterra model of oscillating chemical reactions.

Keywords

• Fuzzy initial value problem
• Sup-J extension principle
• Interactive fuzzy numbers
• Chemical reactions