A numerical method for solving uncertain differential equations

Article type: Research Article

Authors: Yao, Kai | Chen, Xiaowei

Affiliations: Department of Mathematical Sciences, Tsinghua University, Beijing, China | Department of Risk Management and Insurance, Nankai University, Tianjin, China

Note: [] Corresponding author. Xiaowei Chen, Department of Risk Management and Insurance, Nankai University, Tianjin 300071, China. Tel./Fax: +86 22 23505936; E-mail: chenx@nankai.edu.cn

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.

Keywords: Uncertain differential equation, numerical solution, uncertainty theory

DOI: 10.3233/IFS-120688

Journal: Journal of Intelligent & Fuzzy Systems, vol. 25, no. 3, pp. 825-832, 2013