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: 261

Full Length Research Paper

Notes on the order of convergence, consistency and stability properties of newly derived schemes

Sunday Emmanuel Fadugba
  • Sunday Emmanuel Fadugba
  • Department of Mathematics, Faculty of Science, Ekiti State University, Ado Ekiti, Nigeria.
  • Google Scholar

  •  Received: 10 April 2020
  •  Accepted: 14 July 2020
  •  Published: 31 January 2023


In this paper, two numerical integration methods for solving Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs), namely “Third Order One Step Scheme (TOOSS) and Second Order One Step Scheme (SOOSS)” have been considered. The order of convergence, consistency and the stability properties of the schemes have been investigated. From the analyses, it is observed that SOOSS and TOOSS have second order convergence and third order convergence, respectively. It is also observed that both numerical integration methods are consistent and stable. Moreover, three IVPs of stiff differential equations were solved to examine the performance of SOOSS and TOOSS in terms of absolute relative errors. Hence, the numerical results show that TOOSS performs better than SOOSS because of its higher order of accuracy.

Key words: Accuracy, consistency, convergence, final absolute relative error, stability region, stiff differential equation.