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: 252

Full Length Research Paper

Scheme for solving ordinary differential equations with derivative discontinuities: A new class of semi- implicit rational, Runge-Kutta

   Bolarinwa Bolaji1*, Ademiluyi R. A.1,Oluwagunwa A. P.1, Awomuse B. O2   
1Department of Mathematics and Statistics, Rufus Giwa Polytechnic, Owo, Nigeria. 2Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria
Email: [email protected]

  •  Accepted: 06 June 2012
  •  Published: 31 October 2012

Abstract

In this paper, a class of semi- implicit Rational Runge –Kutta scheme is proposed for the integration of differential equations with derivative discontinuities. The method is motivated by varieties of application areas of this class of ordinary differential equations such as electrical transmission network, nuclear reactions, delay problems computer aided designs, economy affected by inflation as well as perturbation problems and dynamic processes in industries and technology fields, and the need to cater for the deficiencies identified in the adoption of the existing methods of solving this class of differential equations. For the development of the scheme, we adopted power series (Taylor and Binomial) expansion, while its analysis and implementation on a micro computer adopts Pade approximation technique and FORTRAN programming respectively. The convergence and stability properties were investigated; it was discovered that the scheme converge and were stable. Numerical result of the adoption of the scheme on some sample problems shows that it is effective and efficient. It compares favourably with modified Euler’s scheme.

Key words: Rational Runge - Kutta, derivative discontinuities, semi - implicit, differential equations.