Fifth-order improved Runge-Kutta method with reduced number of function evaluations

Faranak Rabiei, Fudziah Ismail

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)


The Improved Runge-Kutta (IRK) methods are two step in nature and require lower number of stages per step compared to the classical Runge-Kutta methods. Therefore, the IRK methods will have the lower number of function evaluations per step. Here, the fifth-order Improved Runge-Kutta method (IRK5) with only five stages is derived. The order conditions of the method are obtained up to order six and the coefficients of the fifth order method are determined by minimizing the error norm of the sixth order method. The stability region of the method is presented and numerical examples are given to illustrate the computational efficiency and accuracy of IRK5 compared to RK5.

Original languageEnglish
Pages (from-to)97-105
Number of pages9
JournalAustralian Journal of Basic and Applied Sciences
Issue number3
Publication statusPublished - Mar 2012
Externally publishedYes


  • Improved Runge-Kutta methods
  • Order conditions
  • Ordinary differential equations
  • Stability region
  • Two-step methods

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