IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v425y2022ics0096300322001412.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322001412
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127055?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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. 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.
    4. 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.
    5. 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.
    6. Leonard Dăuş & Ghiocel Groza & Marilena Jianu, 2022. "Full Hermite Interpolation and Approximation in Topological Fields," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
    7. Harendra Singh & Rajesh K. Pandey & Hari Mohan Srivastava, 2019. "Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials," Mathematics, MDPI, vol. 7(3), pages 1-24, February.
    8. Kenzu Abdella & Jeet Trivedi, 2020. "Solving Multi-Point Boundary Value Problems Using Sinc-Derivative Interpolation," Mathematics, MDPI, vol. 8(12), pages 1-14, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001412. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.