Numerical method for solving uncertain spring vibration equation

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.

[1]  Yuanguo Zhu,et al.  Please Scroll down for Article Cybernetics and Systems Uncertain Optimal Control with Application to a Portfolio Selection Model Uncertain Optimal Control with Application to a Portfolio Selection Model , 2022 .

[2]  Baoding Liu.  Fuzzy Process, Hybrid Process and Uncertain Process , 2008 .

[3]  Rong Gao,et al.  Uncertain wave equation with infinite half-boundary , 2017, Appl. Math. Comput..

[4]  Xiaowei Chen,et al.  A numerical method for solving uncertain differential equations , 2013, J. Intell. Fuzzy Syst..

[5]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[6]  Baoding Liu.  Toward uncertain finance theory , 2013 .

[7]  Kai Yao,et al.  Uncertain partial differential equation with application to heat conduction , 2016, Fuzzy Optimization and Decision Making.

[8]  Xiangfeng Yang,et al.  Runge-Kutta Method for Solving Uncertain Differential Equations , 2015 .

[9]  Rong Gao,et al.  Milne method for solving uncertain differential equations , 2016, Appl. Math. Comput..

[10]  Jinwu Gao,et al.  Uncertain differential games with application to capitalism , 2013 .

[11]  Xiangfeng Yang,et al.  Existence and uniqueness theoremfor uncertain spring vibration equation , 2018, J. Intell. Fuzzy Syst..

[12]  Xiangfeng Yang,et al.  Solving uncertain heat equation via numerical method , 2018, Appl. Math. Comput..

[13]  Xiangfeng Yang,et al.  Stability in inverse distribution for uncertain differential equations , 2017, J. Intell. Fuzzy Syst..

[14]  Jinwu Gao,et al.  Linear–Quadratic Uncertain Differential Game With Application to Resource Extraction Problem , 2016, IEEE Transactions on Fuzzy Systems.

[15]  X. Chen,et al.  Existence and uniqueness theorem for uncertain differential equations , 2010, Fuzzy Optim. Decis. Mak..

[16]  Jinwu Gao,et al.  Some stability theorems of uncertain differential equation , 2012, Fuzzy Optimization and Decision Making.

[17]  Baoding Liu.  Some Research Problems in Uncertainty Theory , 2009 .

[18]  Yi Zhang,et al.  Hamming method for solving uncertain differential equations , 2017, Appl. Math. Comput..

[19]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[20]  Xiangfeng Yang,et al.  Existence and uniqueness theorem for uncertain heat equation , 2017, J. Ambient Intell. Humaniz. Comput..

[21]  Dan A. Ralescu,et al.  Adams method for solving uncertain differential equations , 2015, Appl. Math. Comput..

[22]  Xiao Wang,et al.  Adams-Simpson method for solving uncertain differential equation , 2015, Appl. Math. Comput..