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Lidstone-based collocation splines for odd-order BVPs

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  • Costabile, F.A.
  • Gualtieri, M.I.
  • Napoli, A.

Abstract

A method is presented for the numerical solution of odd-order nonlinear boundary value problems with complementary Lidstone boundary conditions. The approximate solution is given in terms of spline interpolation functions, written in the Lidstone second type polynomial basis. Some results on local and global errors are given. Numerical tests are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:186:y:2021:i:c:p:124-135
    DOI: 10.1016/j.matcom.2020.09.002
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. 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.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    4. Francesco Costabile & Anna Napoli, 2012. "Collocation for High-Order Differential Equations with Lidstone Boundary Conditions," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-20, August.
    5. Lamnii, A. & Mraoui, H. & Sbibih, D. & Tijini, A., 2008. "Sextic spline solution of fifth-order boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 237-246.
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    Cited by:

    1. 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.
    2. Dang, Quang A. & Dang, Quang Long & Ngo, T. Kim Quy, 2024. "Numerical methods of fourth, sixth and eighth orders convergence for solving third order nonlinear ODEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 397-414.
    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).
    4. Rufai, Mufutau Ajani & Carpentieri, Bruno & Ramos, Higinio, 2024. "An efficient fifth-order block method for solving third-order BVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 307-321.

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