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Hamming method for solving uncertain differential equations

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  • Zhang, Yi
  • Gao, Jinwu
  • Huang, Zhiyong

Abstract

Uncertain differential equations are important tools to model continuous time varying uncertain phenomena. When analytic solutions become unreachable, numerical solutions provide us important alternatives to solve uncertain differential equations. This paper presents a linear multi-step method, Hamming method, for solving uncertain differential equations. Numerical example shows that the Hamming method is more efficient and effective than the general linear one-step method (e.g. Euler method and Runge–Kutta method). Finally, extreme value and time integral of solutions are also given via Hamming method for illustrating purpose.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:331-341
    DOI: 10.1016/j.amc.2017.05.080
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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. Gao, Rong, 2016. "Milne method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 774-785.
    3. 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.
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    Cited by:

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    3. Liu, Z. & Yang, Y., 2021. "Uncertain pharmacokinetic model based on uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    4. 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.
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    6. 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.
    7. 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.
    8. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
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    11. 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.
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    14. Liu, Z. & Yang, Y., 2021. "Pharmacokinetic model based on multifactor uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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