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A collocation method in spline spaces for the solution of linear fractional dynamical systems

Author

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  • Pellegrino, E.
  • Pezza, L.
  • Pitolli, F.

Abstract

We use a collocation method in refinable spline spaces to solve a linear dynamical system having fractional derivative in time. The method takes advantage of an explicit differentiation rule for the B-spline basis that allows us to efficiently evaluate the collocation matrices appearing in the method. We prove the convergence of the method and show some numerical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:176:y:2020:i:c:p:266-278
    DOI: 10.1016/j.matcom.2019.12.006
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    References listed on IDEAS

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    1. Kolk, Marek & Pedas, Arvet & Tamme, Enn, 2016. "Smoothing transformation and spline collocation for linear fractional boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 234-250.
    2. 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.
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    Cited by:

    1. Noha M. Rasheed & Mohammed O. Al-Amr & Emad A. Az-Zo’bi & Mohammad A. Tashtoush & Lanre Akinyemi, 2021. "Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method," Mathematics, MDPI, vol. 9(16), pages 1-12, August.

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