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Multivalue Collocation Methods for Ordinary and Fractional Differential Equations

Author

Listed:
  • Angelamaria Cardone

    (Department of Mathematics, University of Salerno, 84084 Fisciano, Italy)

  • Dajana Conte

    (Department of Mathematics, University of Salerno, 84084 Fisciano, Italy)

  • Raffaele D’Ambrosio

    (Department of Information Engineering and Computer Science and Mathematics, University of L’Aquila, 67100 L’Aquila, Italy)

  • Beatrice Paternoster

    (Department of Mathematics, University of Salerno, 84084 Fisciano, Italy)

Abstract

The present paper illustrates some classes of multivalue methods for the numerical solution of ordinary and fractional differential equations. In particular, it focuses on two-step and mixed collocation methods, Nordsieck GLM collocation methods for ordinary differential equations, and on two-step spline collocation methods for fractional differential equations. The construction of the methods together with the convergence and stability analysis are reported and some numerical experiments are carried out to show the efficiency of the proposed methods.

Suggested Citation

  • Angelamaria Cardone & Dajana Conte & Raffaele D’Ambrosio & Beatrice Paternoster, 2022. "Multivalue Collocation Methods for Ordinary and Fractional Differential Equations," Mathematics, MDPI, vol. 10(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:185-:d:719924
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    References listed on IDEAS

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    1. Costabile, F.A. & Gualtieri, M.I. & Napoli, A., 2021. "Lidstone-based collocation splines for odd-order BVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 124-135.
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    Cited by:

    1. Francesco Aldo Costabile & Maria Italia Gualtieri & Anna Napoli, 2022. "Polynomial Sequences and Their Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

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