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

Starting the five steps Stomer-Cowell method by Adams-Bashforth method for the solution of the first order ordinary differential equations

Adesanya, A. Olaide
  • Adesanya, A. Olaide
  • Department of Mathematics, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria
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Odekunle, M. R
  • Odekunle, M. R
  • Department of Mathematics, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria
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Alkali, M. Adamu
  • Alkali, M. Adamu
  • Department of Mathematics, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria
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Abubakar, A. Binta
  • Abubakar, A. Binta
  • Department of Mathematics and Statistics, Adamawa State Polytechnic, Yola, Adamawa State, Nigeria
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  •  Accepted: 25 April 2013
  •  Published: 31 May 2013

Abstract

 

We developed a five-step Stomer-Cowell method using method of interpolation and collocation of power series approximate solution to obtain non linear systems of equation which is solved for the unknown parameters to give a continuous linear multi step method. The continuous linear multi-step is evaluated at selected grid points to give discrete linear multi-step method which serve as the corrector. The predictors are developed using the same approach but it is implemented using block method which gives constant order predictors. Basic properties of the corrector viz; order zero stability; convergence and stability interval were verified. The method was tested on some numerical examples and found to give better approximation.

 

Key words: Interpolation, collocation, differential system, order, zero stability, convergence.