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Long time numerical behaviors of fractional pantograph equations

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  • Li, Dongfang
  • Zhang, Chengjian

Abstract

This paper is concerned with long time numerical behaviors of nonlinear fractional pantograph equations. The L1 method with the linear interpolation procedure is applied to solve these nonlinear problems. It is proved that the proposed numerical scheme can inherit the long time behavior of the underlying problems without any stepsize restrictions. After that, the fast evaluation is presented to speed up the calculation of the Caputo fractional derivative. Numerical examples are shown to confirm the theoretical results. Besides, several counter-examples are also given to show that not all the numerical methods can inherit the long time behavior of the underlying problems.

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  • Li, Dongfang & Zhang, Chengjian, 2020. "Long time numerical behaviors of fractional pantograph equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 244-257.
    • Handle: RePEc:eee:matcom:v:172:y:2020:i:c:p:244-257
    DOI: 10.1016/j.matcom.2019.12.004
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    References listed on IDEAS

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    1. Cheng, Xiujun & Duan, Jinqiao & Li, Dongfang, 2019. "A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 452-464.
    2. Yan, Ye & Kou, Chunhai, 2012. "Stability analysis for a fractional differential model of HIV infection of CD4+ T-cells with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1572-1585.
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    Cited by:

    1. Li, Yuyu & Wang, Tongke & Gao, Guang-hua, 2023. "The asymptotic solutions of two-term linear fractional differential equations via Laplace transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 394-412.
    2. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    3. Li, Lili & Zhao, Dan & She, Mianfu & Chen, Xiaoli, 2022. "On high order numerical schemes for fractional differential equations by block-by-block approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    4. Wu, Longbin & Ma, Qiang & Ding, Xiaohua, 2021. "Energy-preserving scheme for the nonlinear fractional Klein–Gordon Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1110-1129.
    5. She, Mianfu & Li, Dongfang & Sun, Hai-wei, 2022. "A transformed L1 method for solving the multi-term time-fractional diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 584-606.
    6. Yao, Zichen & Yang, Zhanwen & Gao, Jianfang, 2023. "Unconditional stability analysis of Grünwald Letnikov method for fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Hafez, Ramy M. & Zaky, Mahmoud A. & Hendy, Ahmed S., 2021. "A novel spectral Galerkin/Petrov–Galerkin algorithm for the multi-dimensional space–time fractional advection–diffusion–reaction equations with nonsmooth solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 678-690.
    8. Ahmed Z. Amin & Mahmoud A. Zaky & Ahmed S. Hendy & Ishak Hashim & Ahmed Aldraiweesh, 2022. "High-Order Multivariate Spectral Algorithms for High-Dimensional Nonlinear Weakly Singular Integral Equations with Delay," Mathematics, MDPI, vol. 10(17), pages 1-20, August.

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