IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/2056834.html
   My bibliography  Save this article

Diagonal Block Method for Solving Two-Point Boundary Value Problems with Robin Boundary Conditions

Author

Listed:
  • Nadirah Mohd Nasir
  • Zanariah Abdul Majid
  • Fudziah Ismail
  • Norfifah Bachok

Abstract

This numerical study presents the diagonal block method of order four for solving the second-order boundary value problems (BVPs) with Robin boundary conditions at two-point concurrently using constant step size. The solution is obtained directly without reducing to a system of first-order differential equations using a combination of predictor-corrector mode via shooting technique. The shooting method was adapted with the Newton divided difference interpolation approach as the strategy of seeking for the new initial estimate. Five numerical examples are included to examine and illustrate the practical usefulness of the proposed method. Numerical tested problem is also highlighted on the diffusion of heat generated application that imposed the Robin boundary conditions. The present findings revealed that the proposed method gives an efficient performance in terms of accuracy, total function calls, and execution time as compared with the existing method.

Suggested Citation

  • Nadirah Mohd Nasir & Zanariah Abdul Majid & Fudziah Ismail & Norfifah Bachok, 2018. "Diagonal Block Method for Solving Two-Point Boundary Value Problems with Robin Boundary Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-12, October.
    • Handle: RePEc:hin:jnlmpe:2056834
    DOI: 10.1155/2018/2056834
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2018/2056834.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2018/2056834.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/2056834?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
    ---><---

    Citations

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


    Cited by:

    1. Nadirah Mohd Nasir & Zanariah Abdul Majid & Fudziah Ismail & Norfifah Bachok, 2019. "Direct Integration of Boundary Value Problems Using the Block Method via the Shooting Technique Combined with Steffensen’s Strategy," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    2. Mohd Nasir, Nadirah & Abdul Majid, Zanariah & Ismail, Fudziah & Bachok, Norfifah, 2021. "Direct integration of the third-order two point and multipoint Robin type boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 411-427.

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnlmpe:2056834. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.