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A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem

Author

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  • M. Mechee
  • N. Senu
  • F. Ismail
  • B. Nikouravan
  • Z. Siri

Abstract

In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method.

Suggested Citation

  • M. Mechee & N. Senu & F. Ismail & B. Nikouravan & Z. Siri, 2013. "A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, June.
    • Handle: RePEc:hin:jnlmpe:795397
    DOI: 10.1155/2013/795397
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    Cited by:

    1. 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.
    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.

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