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Adams–Simpson method for solving uncertain differential equation

Author

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  • Wang, Xiao
  • Ning, Yufu
  • Moughal, Tauqir A.
  • Chen, Xiumei

Abstract

Uncertain differential equation is a type of differential equation driven by canonical Liu process. How to obtain the analytic solution of uncertain differential equation has always been a thorny problem. In order to solve uncertain differential equation, early researchers have proposed two numerical algorithms based on Euler method and Runge–Kutta method. This paper will design another numerical algorithm for solving uncertain differential equations via Adams–Simpson method. Meanwhile, some numerical experiments are given to illustrate the efficiency of the proposed numerical algorithm. Furthermore, this paper gives how to calculate the expected value, the inverse uncertainty distributions of the extreme value and the integral of the solution of uncertain differential equation with the aid of Adams–Simpson method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:209-219
    DOI: 10.1016/j.amc.2015.09.009
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    Citations

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    Cited by:

    1. Wang, Xiao & Ning, Yufu & Peng, Zhen, 2020. "Some results about uncertain differential equations with time-dependent delay," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    2. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. 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.
    4. Jia, Lifen & Chen, Wei, 2020. "Knock-in options of an uncertain stock model with floating interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. 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.
    6. Yiyao Sun & Taoyong Su, 2017. "Mean-reverting stock model with floating interest rate in uncertain environment," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 235-255, June.
    7. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    8. 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.
    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. 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.
    11. Yang, Xiangfeng, 2018. "Solving uncertain heat equation via numerical method," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 92-104.
    12. Lu, Ziqiang & Zhu, Yuanguo, 2019. "Numerical approach for solution to an uncertain fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 137-148.
    13. Lu, Ziqiang & Zhu, Yuanguo, 2023. "Asymptotic stability in pth moment of uncertain dynamical systems with time-delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 323-335.

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