High-order Uncertain Differential Equation and Its Application to Nuclear Reactors

TL;DR

This paper introduces a rigorous method for solving high-order uncertain differential equations and demonstrates its application to nuclear reactor kinetics, correcting previous solution approaches.

Contribution

It provides a new, accurate solution method for HUDE, including parameter estimation and hypothesis testing, with a specific application to nuclear reactors.

Findings

Proved comparison theorems for high-order differential equations

Developed a solution method for HUDE including parameter estimation

Applied the method successfully to nuclear reactor kinetics

Abstract

High-order uncertain differential equation (HUDE) was introduced in literature. But the present method to solve a HUDE is incorrect. In this paper, we will rigorously prove some comparion theorems of high-order differential equations, and present a method to solve a family of HUDE, including parameter estimation and hypothesis test. Then an application to nuclear reactor kinetics is given to illustrate the method.