Adams predictor–corrector method for solving uncertain differential equation

Uncertain differential equation (UDE) is a type of differential equation driven by Liu process, which is used to describe uncertain dynamic systems. Since the analytic solution of UDE is difficult to obtain or the representation is complex, this paper proposes a new Adams predictor–corrector method to solve UDE. Compared with Euler Method, Runge–Kutta method, Adams method, Milne method, Adam–Simpson method and Hamming method of solving UDE, the proposed algorithm has higher accuracy. The extreme value and time integral of solution to UDE are obtained in virtue of the proposed method. Meanwhile, the convergence properties of the method are discussed. Finally, some illustrated examples are provided to demonstrate the efficiency and accuracy of the proposed technique.