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: 262

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

References

Agam SA (2014). Sixth order singly and Multiply Runge-kutta method for first and higher order ODEs (PhD thesis in preparation) NDA Kaduna.
 
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Butcher JC, Jackiewicz Z (1998). Construction of high order diagonally implicit multi-stage Integration methods for ODEs. Appl. Numer. Math. 27:1-12
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Hairer E, Warnner G (1996). Solving ODEs II stiff and differential-algebraic problems. Berlin Heldelberg, New York, Springer verlaf.
 
Kuntzmann J (1961). Neume entwickhingent der methoden von Runge and Kutta, Z Angew. Math. Mech. 41:T28-T31.
 
Onumanyi P, Awoyemi DO, Jator SN, Siriseria UW (1994). New Linear Multistep Methods with Continuous coefficients for First Order IVPs. J. Niger. Math. Soc. 13:37- 51.
 
Petzol I (1981). An efficient numerical method for highly oscillatory ODEs. SIAM J. Numer. Anal. 18:455-479.
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Press WH, Flennery, Briain P, Teukolsky, Soul A, Vetterling WT (2007). Runge-Kutta methods. Numerical Recipes: The Art of scientific computing (3rd ed) Cambridge University press ISSN 978-0-521-88068-8. p. 907.
 
Yakubu DG (2010). Uniform accurate order five Radau-Runge-Kutta collocation methods. J. Math. Assoc. Niger. 37(2):75-94.

 

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