IDEAS home Printed from https://ideas.repec.org/a/wly/jnlmpe/v2023y2023i1n5754475.html

A 14‐Order Hybrid Block Method in Variable Step‐Size Mode for Solving Second‐Order Initial Value Problems

Author

Listed:
  • Samuel N. Jator
  • Higinio Ramos
  • Mark I. Modebei

Abstract

The search for efficient higher order methods is a constant goal in numerical analysis. In this paper, a higher order two‐step hybrid block method is presented to directly solve second‐order initial value problems in ordinary differential equations. In addition to the higher order, the proposed method has been formulated in variable step‐size mode to extract its best performance. Comparisons with other methods in the literature show the good accuracy it can provide. Theoretical aspects such as linear stability and convergence analysis are also discussed.

Suggested Citation

  • Samuel N. Jator & Higinio Ramos & Mark I. Modebei, 2023. "A 14‐Order Hybrid Block Method in Variable Step‐Size Mode for Solving Second‐Order Initial Value Problems," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:5754475
    DOI: 10.1155/2023/5754475
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2023/5754475
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/5754475?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
    ---><---

    References listed on IDEAS

    as
    1. Ch. TSITOURAS, 2006. "Explicit Eighth Order Two-Step Methods With Nine Stages For Integrating Oscillatory Problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(06), pages 861-876.
    2. Ramos, Higinio & Singh, Gurjinder & Kanwar, V. & Bhatia, Saurabh, 2016. "An efficient variable step-size rational Falkner-type method for solving the special second-order IVP," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 39-51.
    3. Higinio Ramos & Samuel N. Jator & Mark I. Modebei, 2020. "Efficient k -Step Linear Block Methods to Solve Second Order Initial Value Problems Directly," Mathematics, MDPI, vol. 8(10), pages 1-17, October.
    4. Samuel N. Jator & Kindyl L. King, 2018. "Integrating Oscillatory General Second-Order Initial Value Problems Using a Block Hybrid Method of Order 11," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-15, June.
    Full references (including those not matched with items on IDEAS)

    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. Higinio Ramos & Ridwanulahi Abdulganiy & Ruth Olowe & Samuel Jator, 2021. "A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions," Mathematics, MDPI, vol. 9(7), pages 1-22, March.
    2. Sunday, Joshua & Shokri, Ali & Mahwash Kamoh, Nathaniel & Cleofas Dang, Bwebum & Idrisoglu Mahmudov, Nazim, 2024. "A computational approach to solving some applied rigid second-order problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 121-138.
    3. Tsitouras, Ch., 2014. "On fitted modifications of Runge–Kutta–Nyström pairs," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 416-423.
    4. Vladislav N. Kovalnogov & Ruslan V. Fedorov & Andrey V. Chukalin & Theodore E. Simos & Charalampos Tsitouras, 2021. "Eighth Order Two-Step Methods Trained to Perform Better on Keplerian-Type Orbits," Mathematics, MDPI, vol. 9(23), pages 1-19, November.
    5. Ramos, Higinio & Rufai, M.A., 2018. "Third derivative modification of k-step block Falkner methods for the numerical solution of second order initial-value problems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 231-245.
    6. Higinio Ramos & Samuel N. Jator & Mark I. Modebei, 2020. "Efficient k -Step Linear Block Methods to Solve Second Order Initial Value Problems Directly," Mathematics, MDPI, vol. 8(10), pages 1-17, October.
    7. Singh, Gurjinder & Garg, Arvind & Kanwar, V. & Ramos, Higinio, 2019. "An efficient optimized adaptive step-size hybrid block method for integrating differential systems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    8. Ramos, Higinio & Rufai, M.A., 2019. "A third-derivative two-step block Falkner-type method for solving general second-order boundary-value systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 139-155.
    9. Reem Allogmany & Fudziah Ismail, 2020. "Implicit Three-Point Block Numerical Algorithm for Solving Third Order Initial Value Problem Directly with Applications," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    10. Denis Butusov, 2021. "Adaptive Stepsize Control for Extrapolation Semi-Implicit Multistep ODE Solvers," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    11. Obaid Alshammari & Sondess Ben Aoun & Mourad Kchaou & Theodore E. Simos & Charalampos Tsitouras & Houssem Jerbi, 2024. "Eighth-Order Numerov-Type Methods Using Varying Step Length," Mathematics, MDPI, vol. 12(14), pages 1-14, July.
    12. Rubayyi T. Alqahtani & Theodore E. Simos & Charalampos Tsitouras, 2025. "Ninth-Order Two-Step Methods with Varying Step Lengths," Mathematics, MDPI, vol. 13(8), pages 1-15, April.
    13. Vladislav N. Kovalnogov & Ruslan V. Fedorov & Tamara V. Karpukhina & Theodore E. Simos & Charalampos Tsitouras, 2021. "Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions," Mathematics, MDPI, vol. 9(21), pages 1-12, October.

    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:wly:jnlmpe:v:2023:y:2023:i:1:n:5754475. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/2629 .

    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.