Solution of First Order Initial Value Problem using Analytical and Numerical Method in Neutrosophic Environment

Abstract

In this paper, the solution of a first-order linear non-homogeneous fuzzy differential equation with an initial condition is described in a neutrosophic environment. For this purpose, using triangular neutrosophic numbers, the neutrosophic analytical method, and the fourth-order Runge-Kutta numerical method have been introduced for solving fuzzified first order differential equation. We also observed solutions at the (α,β,γ)-cut with varied time scales. In addition, the error between the analytical and numerical solution obtained on the (α,β,γ)-cut is evaluated and illustrated using tables with varying time. A good amount of agreement is seen using closed form and numerical solutions.

Keywords

• differential equation
• fuzzy set
• triangular fuzzy numbers
• neutrosophic
• runge-kutta 4th order