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Fourth-Order Improved Runge–Kutta Method for Directly Solving Special Third-Order Ordinary Differential Equations

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Abstract

In this paper, fourth-order improved Runge–Kutta method (IRKD) for directly solving a special third-order ordinary differential equation is constructed. The fourth-order IRKD method has a lower number of function evaluations compared with the fourth-order Runge–Kutta method. The stability polynomial of the method is given. Numerical comparisons are also performed using the existing Runge–Kutta method after reducing the problems into a system of first-order equations and solving them, and direct RKD method for solving special third-order ordinary differential equations. Numerical examples are presented to illustrate the efficiency and the accuracy of the new method in terms of number of function evaluations as well as max absolute error.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM, 43400, Serdang, Selangor, Malaysia

    Kasim Abbas Hussain, Fudziah Ismail, Norazak Senu & Faranak Rabiei

  2. Institute for Mathematical Research, Universiti Putra Malaysia, UPM, 43400, Serdang, Selangor, Malaysia

    Fudziah Ismail, Norazak Senu & Faranak Rabiei

  3. Department of Mathematics, College of Science, Al-Mustansiriyah University, Baghdad, Iraq

    Kasim Abbas Hussain

Authors
  1. Kasim Abbas Hussain
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  2. Fudziah Ismail
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  3. Norazak Senu
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  4. Faranak Rabiei
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Correspondence to Kasim Abbas Hussain.

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Hussain, K.A., Ismail, F., Senu, N. et al. Fourth-Order Improved Runge–Kutta Method for Directly Solving Special Third-Order Ordinary Differential Equations. Iran J Sci Technol Trans Sci 41, 429–437 (2017). https://doi.org/10.1007/s40995-017-0258-1

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  • DOI: https://doi.org/10.1007/s40995-017-0258-1

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