A numerical method for solving uncertain differential equations

被引：331
作者：
Yao, Kai [1 ]
Chen, Xiaowei [2 ]
机构：
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Nankai Univ, Dept Risk Management & Insurance, Tianjin 300071, Peoples R China
来源：
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS | 2013年 / 25卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Uncertain differential equation; numerical solution; uncertainty theory;
D O I：
10.3233/IFS-120688
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Uncertain differential equation is a type of differential equation driven by canonical process. In this paper, a concept of alpha-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 alpha-path and produces an inverse uncertainty distribution of the solution. To illustrate the efficiency of the numerical method, several examples are given.
引用
收藏
页码：825 / 832
页数：8
相关论文
共 21 条
[1]  
[Anonymous], 1955, Rendiconti del Circolo Matematico di Palermo, DOI DOI 10.1007/BF02846028
[2]   Existence and uniqueness theorem for uncertain differential equations [J].
Chen, X. ;
Liu, B. .
FUZZY OPTIMIZATION AND DECISION MAKING, 2010, 9 (01) :69-81
[3]   Cross-entropy measure of uncertain variables [J].
Chen, Xiaowei ;
Kar, Samarjit ;
Ralescu, Dan A. .
INFORMATION SCIENCES, 2012, 201 :53-60
[4]   ON LIU'S INFERENCE RULE FOR UNCERTAIN SYSTEMS [J].
Gao, Xin ;
Gao, Yuan ;
Ralescu, Dan A. .
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 2010, 18 (01) :1-11
[5]  
Li X, 2008, J INTELL FUZZY SYST, V19, P197
[6]  
Liu B., 2007, Uncertainty theory, V2nd, DOI DOI 10.1007/978-3-642-13959-8
[7]  
Liu B., 2009, J. Uncertain Syst., V3, P3
[8]  
Liu B., 2008, J. Uncertain Syst., V2, P3
[9]  
Liu Y., 2012, J UNCERTAIN SYST, V6, P243, DOI DOI 10.1007/S11166-012-9141-9
[10]  
Liu Y., UNCERTAIN CURRENCY M
123