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Numerical solution of fourth-order BVPs by using Lidstone-collocation method

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  • Moghadam, Amin Abrishami
  • Soheili, Ali R.
  • Bagherzadeh, Amir Saboor

Abstract

In this paper, a new method for solving fourth-order BVPs is presented. The method is based on the first type Lidstone interpolating function. One of the greatest features of the Lidstone interpolating function is that, it can be extended to a piecewise function. Therefore, this extension led us construct piecewise Lidstone interpolating functions on the subintervals and subsequently on the collocation points to have better accuracy. We have fully discussed the method and the whole process in full details to obtain a large system of algebraic equations. The system includes numerical approximation of the problems at the collocation points. From the aspect of error estimation, we have obtained the local truncation errors of the equations and finally presented the comparisons of our approach with the other methods.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001412
    DOI: 10.1016/j.amc.2022.127055
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    References listed on IDEAS

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    1. Xu, Lan, 2009. "The variational iteration method for fourth order boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1386-1394.
    2. Mehdi Dehghan & Mehdi Tatari, 2006. "The use of Adomian decomposition method for solving problems in calculus of variations," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-12, June.
    3. 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.
    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. Omer Kelesoglu, 2014. "The Solution of Fourth Order Boundary Value Problem Arising out of the Beam-Column Theory Using Adomian Decomposition Method," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, March.
    6. 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. Ana Maria Acu & Ioan Raşa & Ancuţa Emilia Şteopoaie, 2022. "Algebraic Systems with Positive Coefficients and Positive Solutions," Mathematics, MDPI, vol. 10(8), pages 1-10, April.

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