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A block hybrid integrator for numerically solving fourth-order Initial Value Problems

Author

Listed:
  • Modebei, Mark I.
  • Adeniyi, Rapheal B.
  • Jator, Samuel N.
  • Ramos, Higinio

Abstract

A Linear Multistep Hybrid Block method with four intra-step grid points is presented for approximating directly the solution of fourth order Initial Value Problems (IVPs). Multiple Finite Difference formulas are derived and combined in a block formulation to form a numerical integrator that provides direct solution to fourth order IVPs over sub-intervals. The properties and convergence of the proposed method are discussed. The superiority of this method over existing methods is established numerically on different test problems.

Suggested Citation

  • Modebei, Mark I. & Adeniyi, Rapheal B. & Jator, Samuel N. & Ramos, Higinio, 2019. "A block hybrid integrator for numerically solving fourth-order Initial Value Problems," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 680-694.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:680-694
    DOI: 10.1016/j.amc.2018.10.080
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    References listed on IDEAS

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    1. Lee Ken Yap & Fudziah Ismail & Norazak Senu, 2014. "An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, May.
    2. T. A. Biala, 2016. "A Computational Study of the Boundary Value Methods and the Block Unification Methods for," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-14, April.
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    Cited by:

    1. Janez Urevc & Miroslav Halilovič, 2021. "Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs," Mathematics, MDPI, vol. 9(2), pages 1-21, January.
    2. Khalsaraei, Mohammad Mehdizadeh & Shokri, Ali & Ramos, Higinio & Heydari, Shahin, 2021. "A positive and elementary stable nonstandard explicit scheme for a mathematical model of the influenza disease," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 397-410.

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