Numerical method for solving uncertain spring vibration equation

Lifen Jia, Waichon Lio and Xiangfeng Yang

Applied Mathematics and Computation, 2018, vol. 337, issue C, 428-441

Abstract: 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.

Keywords: Spring vibration equation; Uncertain differential equation; Uncertainty theory; Uncertain process (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:337:y:2018:i:c:p:428-441

DOI: 10.1016/j.amc.2018.05.045

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