African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Full Length Research Paper

A highly efficient implicit Runge-Kutta method for first order ordinary differential equations

S. A. Agam
  • S. A. Agam
  • Department of Mathematics and Computer Science, Nigerian Defence Academy, Kaduna, Nigeria.
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Y. A. Yahaya
  • Y. A. Yahaya
  • Department of Mathematics and Computer Science, Federal University of Technology Minna, Nigeria.
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  •  Received: 08 April 2014
  •  Accepted: 16 June 2014
  •  Published: 23 July 2014


In this paper we develop a more efficient three-stage implicit Runge-Kutta method of order 6 for solving first order initial value problems of ordinary differential equations. Collocation method is used to derive Continuous schemes in which both the interpolation and collocation points are at perturbed Gaussian points. This gives a higher order scheme, which is more efficient and stable than the existing similar ones. Simple linear problems are used to check its level of accuracy and stability.


Key words: Implicit, more efficient, stable, collocation methods, Perturbed Gaussian points and error estimates.