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Cubic Lidstone-Spline for numerical solution of BVPs

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  • Costabile, Francesco A.
  • Gualtieri, Maria Italia
  • Serafini, Giada

Abstract

A new collocation method based on cubic Lidstone Splines is introduced for solving second order BVPs. It derives directly from piecewise Lidstone polynomials of degree 3 by requiring the continuity of the first derivative at the nodal points. For equally spaced nodes it reduces to a classical finite difference method of second order. The estimation of local and global error is given. Finally we solve some numerical problems and we compare the results with those of other methods.

Suggested Citation

  • Costabile, Francesco A. & Gualtieri, Maria Italia & Serafini, Giada, 2017. "Cubic Lidstone-Spline for numerical solution of BVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 56-64.
    • Handle: RePEc:eee:matcom:v:141:y:2017:i:c:p:56-64
    DOI: 10.1016/j.matcom.2017.01.006
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    References listed on IDEAS

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    1. Manni, Carla & Mazzia, Francesca & Sestini, Alessandra & Speleers, Hendrik, 2015. "BS2 methods for semi-linear second order boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 147-156.
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    Cited by:

    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.
    2. Tafakkori–Bafghi, M. & Loghmani, G.B. & Heydari, M., 2022. "Numerical solution of two-point nonlinear boundary value problems via Legendre–Picard iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 133-159.
    3. Moghadam, Amin Abrishami & Soheili, Ali R. & Bagherzadeh, Amir Saboor, 2022. "Numerical solution of fourth-order BVPs by using Lidstone-collocation method," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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