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Smoothing transformation and spline collocation for linear fractional boundary value problems

Author

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  • Kolk, Marek
  • Pedas, Arvet
  • Tamme, Enn

Abstract

We construct and justify a high order method for the numerical solution of multi-point boundary value problems for linear multi-term fractional differential equations involving Caputo-type fractional derivatives. Using an integral equation reformulation of the boundary value problem we first regularize the solution by a suitable smoothing transformation. After that we solve the transformed equation by a piecewise polynomial collocation method on a mildly graded or uniform grid. Optimal global convergence estimates are derived and a superconvergence result for a special choice of collocation parameters is established. To illustrate the reliability of the proposed method some numerical results are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:234-250
    DOI: 10.1016/j.amc.2016.02.044
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    Cited by:

    1. 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.
    2. 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.

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