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Runge-Kutta Type Methods for Directly Solving Special Fourth-Order Ordinary Differential Equations

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  • Kasim Hussain
  • Fudziah Ismail
  • Norazak Senu

Abstract

A Runge-Kutta type method for directly solving special fourth-order ordinary differential equations (ODEs) which is denoted by RKFD method is constructed. The order conditions of RKFD method up to order five are derived; based on the order conditions, three-stage fourth- and fifth-order Runge-Kutta type methods are constructed. Zero-stability of the RKFD method is proven. Numerical results obtained are compared with the existing Runge-Kutta methods in the scientific literature after reducing the problems into a system of first-order ODEs and solving them. Numerical results are presented to illustrate the robustness and competency of the new methods in terms of accuracy and number of function evaluations.

Suggested Citation

  • Kasim Hussain & Fudziah Ismail & Norazak Senu, 2015. "Runge-Kutta Type Methods for Directly Solving Special Fourth-Order Ordinary Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, August.
    • Handle: RePEc:hin:jnlmpe:893763
    DOI: 10.1155/2015/893763
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    Cited by:

    1. Higinio Ramos & Samuel N. Jator & Mark I. Modebei, 2020. "Efficient k -Step Linear Block Methods to Solve Second Order Initial Value Problems Directly," Mathematics, MDPI, vol. 8(10), pages 1-17, October.

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