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Numerical method for solving uncertain spring vibration equation

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  • Jia, Lifen
  • Lio, Waichon
  • Yang, Xiangfeng

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.

Suggested Citation

  • Jia, Lifen & Lio, Waichon & Yang, Xiangfeng, 2018. "Numerical method for solving uncertain spring vibration equation," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 428-441.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:428-441
    DOI: 10.1016/j.amc.2018.05.045
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    References listed on IDEAS

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    1. Yang, Xiangfeng & Ralescu, Dan A., 2015. "Adams method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 993-1003.
    2. Andrzej Ruszczynski & Jianing Yao, 2017. "A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation," Papers 1701.06234, arXiv.org, revised Aug 2020.
    3. Yang, Xiangfeng, 2018. "Solving uncertain heat equation via numerical method," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 92-104.
    4. Wang, Xiao & Ning, Yufu & Moughal, Tauqir A. & Chen, Xiumei, 2015. "Adams–Simpson method for solving uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 209-219.
    5. Gao, Rong, 2016. "Milne method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 774-785.
    6. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
    7. Zhang, Yi & Gao, Jinwu & Huang, Zhiyong, 2017. "Hamming method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 331-341.
    8. Gao, Rong, 2017. "Uncertain wave equation with infinite half-boundary," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 28-40.
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    Citations

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    Cited by:

    1. Yang, Xiangfeng & Ralescu, Dan A., 2021. "A Dufort–Frankel scheme for one-dimensional uncertain heat equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 98-112.
    2. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    3. Jia, Lifen & Sheng, Yuhong, 2019. "Stability in distribution for uncertain delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 49-56.
    4. Abdulsalam, Athraa & Senu, Norazak & Majid, Zanariah Abdul & Long, Nik Mohd Asri Nik, 2024. "Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 104-125.
    5. Chen, Xin & Zhu, Yuanguo & Sheng, Linxue, 2021. "Optimal control for uncertain stochastic dynamic systems with jump and application to an advertising model," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    6. Shen, Jiayu, 2020. "An uncertain sustainable supply chain network," Applied Mathematics and Computation, Elsevier, vol. 378(C).

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