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Numerical method for solving uncertain spring vibration equation
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DOI：10.1016/j.amc.2018.05.045.png)
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Abstract
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As a type of uncertain differential equations, uncertain spring vibration equation is driven by Liu process. This paper proposes a concept of alpha-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 alpha-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. (C) 2018 Elsevier Inc. All rights reserved.
Keywords:
Spring vibration equation
Uncertain differential equation
Uncertainty theory
Uncertain process
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