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Milne method for solving uncertain differential equations

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  • Gao, Rong

Abstract

Uncertain differential equation is a type of differential equation driven by Liu process and has been widely applied to many fields especially to uncertain finance. Unfortunately, the analytic solutions of uncertain differential equations cannot always be obtained. So far, some numerical methods have been investigated. This paper designs a new numerical algorithm for solving uncertain differential equations via Milne method.

Suggested Citation

  • Gao, Rong, 2016. "Milne method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 774-785.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:774-785
    DOI: 10.1016/j.amc.2015.11.043
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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. 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.
    3. 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.
    4. 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).
    5. Lifen Jia & Wei Chen, 2021. "Uncertain SEIAR model for COVID-19 cases in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 243-259, June.
    6. Gao, Rong, 2019. "Stability in mean for uncertain differential equation with jumps," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 15-22.
    7. Gao, Rong & Ma, Nana & Sun, Gaoji, 2019. "Stability of solution for uncertain wave equation," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 469-478.
    8. Gao, Rong, 2017. "Uncertain wave equation with infinite half-boundary," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 28-40.
    9. Yang, Xiangfeng, 2018. "Solving uncertain heat equation via numerical method," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 92-104.
    10. 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.
    11. Jia, Lifen & Chen, Wei, 2020. "Knock-in options of an uncertain stock model with floating interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    12. Rong Gao, 2022. "Almost Sure Stability for Multi-Dimensional Uncertain Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-10, September.
    13. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    14. Weiwei Wang & Dan A. Ralescu, 2021. "Option pricing formulas based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 471-495, December.
    15. 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.
    16. Gao, Rong & Hua, Kexin, 2023. "A numerical method for solving uncertain wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    17. 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.
    18. Rong Gao & Yan Sun & Dan A. Ralescu, 2017. "Order statistics of uncertain random variables with application to k-out-of-n system," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 159-181, June.
    19. 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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