1. Numerical method for solving uncertain spring vibration equation.
- Author
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Jia, Lifen, Lio, Waichon, and Yang, Xiangfeng
- Subjects
- *
NUMERICAL analysis , *VIBRATION (Mechanics) , *DIFFERENTIAL equations , *MATHEMATICAL analysis , *MATHEMATICAL models - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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