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Quadratic spline collocation method for the time fractional subdiffusion equation

Author

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  • Luo, Wei-Hua
  • Huang, Ting-Zhu
  • Wu, Guo-Cheng
  • Gu, Xian-Ming

Abstract

In this paper, exploiting the quadratic spline collocation (QSC) method, we numerically solve the time fractional subdiffusion equation with Dirichelt boundary value conditions. The coefficient matrix of the discretized linear system is investigated in detail. Theoretical analyses and numerical examples demonstrate the proposed technique can enjoy the global error bound with O(τ3+h3) under the L∞ norm provided that the solution v(x, t) has four-order continual derivative with respects to x and t, and it can achieve the accuracy of O(τ4+h4) at collocation points, where τ, h are the step sizes in time and space, respectively.

Suggested Citation

  • Luo, Wei-Hua & Huang, Ting-Zhu & Wu, Guo-Cheng & Gu, Xian-Ming, 2016. "Quadratic spline collocation method for the time fractional subdiffusion equation," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 252-265.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:252-265
    DOI: 10.1016/j.amc.2015.12.020
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    References listed on IDEAS

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    1. Chen, S. & Liu, F. & Jiang, X. & Turner, I. & Anh, V., 2015. "A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 591-601.
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    Cited by:

    1. Luo, Wei-Hua & Gu, Xian-Ming & Carpentieri, Bruno, 2022. "A hybrid triangulation method for banded linear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 97-108.
    2. Zhao, Yong-Liang & Zhu, Pei-Yong & Luo, Wei-Hua, 2018. "A fast second-order implicit scheme for non-linear time-space fractional diffusion equation with time delay and drift term," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 231-248.
    3. Pezza, L. & Pitolli, F., 2018. "A multiscale collocation method for fractional differential problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 210-219.
    4. Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
    5. Kashfi Sadabad, Mahnaz & Jodayree Akbarfam, Aliasghar, 2021. "An efficient numerical method for estimating eigenvalues and eigenfunctions of fractional Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 547-569.
    6. Sarita Gajbhiye Meshram & Vijay P. Singh & Ozgur Kisi & Chandrashekhar Meshram, 2021. "Soil erosion modeling of watershed using cubic, quadratic and quintic splines," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(3), pages 2701-2719, September.
    7. Sowa, Marcin, 2018. "Application of SubIval in solving initial value problems with fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 86-103.
    8. Wang, Yihong & Cao, Jianxiong, 2021. "A tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity," Applied Mathematics and Computation, Elsevier, vol. 401(C).

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