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A New Integrator for Special Third Order Differential Equations With Application to Thin Film Flow Problem

Author

Listed:
  • Y. D. Jikantoro

    (University Putra Malaysia
    Ibrahim Badamasi Babangida University)

  • F. Ismail

    (University Putra Malaysia
    University Putra Malaysia)

  • N. Senu

    (University Putra Malaysia
    University Putra Malaysia)

  • Z. B. Ibrahim

    (University Putra Malaysia
    University Putra Malaysia)

Abstract

In recent time, Runge-Kutta methods that integrate special third order ordinary differential equations (ODEs) directly are proposed to address efficiency issues associated with classical Runge-Kutta methods. Albeit, the methods require evaluation of three set of equations to proceed with the numerical integration. In this paper, we propose a class of multistep-like Runge-Kutta methods (hybrid methods), which integrates special third order ODEs directly. The method is completely derivative-free. Algebraic order conditions of the method are derived. Using the order conditions, a four-stage method is presented. Numerical experiment is conducted on some test problems. The method is also applied to a practical problem in Physics and engineering to ascertain its validity. Results from the experiment show that the new method is more accurate and efficient than the classical Runge-Kutta methods and a class of direct Runge-Kutta methods recently designed for special third order ODEs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:49:y:2018:i:1:d:10.1007_s13226-018-0259-6
    DOI: 10.1007/s13226-018-0259-6
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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.
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