A numerical method for solving uncertain differential equations

Abstract

Uncertain differential equation is a type of differential equation driven by canonical process. In this paper, a concept of α-path to uncertain differential equation is first introduced, which is a type of deterministic function that solves an associate ordinary differential equation. Then, a numerical method is designed for solving uncertain differential equations, which essentially solves each α-path and produces an inverse uncertainty distribution of the solution. To illustrate the efficiency of the numerical method, several examples are given.