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A multiscale collocation method for fractional differential problems

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  • Pezza, L.
  • Pitolli, F.

Abstract

We introduce a multiscale collocation method to numerically solve differential problems involving both ordinary and fractional derivatives of high order. The proposed method uses multiresolution analyses (MRA) as approximating spaces and takes advantage of a finite difference formula that allows us to express both ordinary and fractional derivatives of the approximating function in a closed form. Thus, the method is easy to implement, accurate and efficient. The convergence and the stability of the multiscale collocation method are proved and some numerical results are shown.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:147:y:2018:i:c:p:210-219
    DOI: 10.1016/j.matcom.2017.07.005
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Xie, Jiaquan & Wang, Tao & Ren, Zhongkai & Zhang, Jun & Quan, Long, 2019. "Haar wavelet method for approximating the solution of a coupled system of fractional-order integral–differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 80-89.
    2. Pellegrino, E. & Pezza, L. & Pitolli, F., 2020. "A collocation method in spline spaces for the solution of linear fractional dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 266-278.

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