The α-path of multi-dimensional uncertain differential equations and its applications

Abstract

As a complex uncertain differential equation, how to solve the multi-dimensional uncertain differential equation is a complicated and difficult problem. This paper will be devoted to the α-path of some special multi-dimensional uncertain differential equations, namely, multi-factor uncertain differential equations, nested uncertain differential equations and multi-factor nested uncertain differential equations. The α-path method is used to study the numerical solution problems of the above three special multi-dimensional uncertain differential equations. At the same time, the inverse uncertainty distributions and expected values of these three special multi-dimensional uncertain differential equations are also obtained. At last, the numerical algorithm examples are given to verify it.