Numerical method for solving uncertain spring vibration equation

As a type of uncertain differential equations, uncertain spring vibration equation is driven by Liu process. This paper proposes a concept of α-path, and shows that the solution of an uncertain spring vibration equation can be expressed by a family of solutions of second-order ordinary differential...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics and computation 2018-11, Vol.337, p.428-441
Main Authors: Jia, Lifen, Lio, Waichon, Yang, Xiangfeng
Format: Article
Language:English
Subjects:
Spring vibration equation
Uncertain differential equation
Uncertain process
Uncertainty theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:As a type of uncertain differential equations, uncertain spring vibration equation is driven by Liu process. This paper proposes a concept of α-path, and shows that the solution of an uncertain spring vibration equation can be expressed by a family of solutions of second-order ordinary differential equations. This paper also proves that the inverse uncertainty distribution of solution of uncertain spring vibration equation is just the α-path of uncertain spring vibration equation, and a numerical algorithm is designed. Moreover, a formula to calculate the expected value of solution of uncertain spring vibration equation is derived. Finally, several numerical examples are provided to illustrate the efficiency of the numerical method.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.05.045