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Analysis of simple pendulum with uncertain differential equation

Author

Listed:
  • Xie, Jinsheng
  • Lio, Waichon
  • Kang, Rui

Abstract

Uncertain differential equation is a type of differential equation involving uncertain processes. This paper analyzes a simple pendulum system with a varying drag coefficient by the tool of uncertain differential equation, and derives the uncertain simple pendulum equation. Afterwards, the numerical method of solving the uncertain simple pendulum equation and its parameter estimation method are given in this paper. Finally, a real-world example is provided to illustrate the uncertain simple pendulum equation.

Suggested Citation

  • Xie, Jinsheng & Lio, Waichon & Kang, Rui, 2024. "Analysis of simple pendulum with uncertain differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924006970
    DOI: 10.1016/j.chaos.2024.115145
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    References listed on IDEAS

    as
    1. Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    2. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    3. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Yu, Yongjiu & Yang, Xiangfeng & Lei, Qing, 2022. "Pricing of equity swaps in uncertain financial market," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Lu, Jing & Yang, Xiangfeng & Tian, Miao, 2022. "Barrier swaption pricing formulae of mean-reverting model in uncertain environment," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Waichon Lio & Baoding Liu, 2021. "Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 177-188, June.
    7. Gao, Rong & Hua, Kexin, 2023. "A numerical method for solving uncertain wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    8. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    9. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. 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.
    Full references (including those not matched with items on IDEAS)

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