Abstract
Uncertain differential equation is a type of differential equation involving uncertain processes. This chapter will discuss the existence, uniqueness and stability of solutions of uncertain differential equations, and introduce Yao-Chen formula that represents the solution of an uncertain differential equation by a family of solutions of ordinary differential equations. On the basis of this formula, some formulas to calculate extreme value, first hitting time, and time integral of solution are provided. Furthermore, some numerical methods for solving general uncertain differential equations are designed.
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