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An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations

Author

Listed:
  • Lee Ken Yap
  • Fudziah Ismail
  • Norazak Senu

Abstract

The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:549597
    DOI: 10.1155/2014/549597
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    Cited by:

    1. 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.
    2. Emilio Defez & Javier Ibáñez & José M. Alonso & Michael M. Tung & Teresa Real-Herráiz, 2021. "On the Approximated Solution of a Special Type of Nonlinear Third-Order Matrix Ordinary Differential Problem," Mathematics, MDPI, vol. 9(18), pages 1-18, September.
    3. Y. D. Jikantoro & F. Ismail & N. Senu & Z. B. Ibrahim, 2018. "A New Integrator for Special Third Order Differential Equations With Application to Thin Film Flow Problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(1), pages 151-167, March.
    4. 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.

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