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: 233

Full Length Research Paper

Derivation of a new block fifth order method for numerical solution of first order initial value problems

Salman H. Abbas
  • Salman H. Abbas
  • Department of Mathematical Sciences, College of Arts and Science, Ahlia University, P. O. Box 10887, Kingdom of Bahrain.
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Noor A. Jalil Alshakhoori
  • Noor A. Jalil Alshakhoori
  • Department of Mathematics, College of Science, University of Bahrain, P. O. Box 32038, Kingdom of Bahrain.
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  •  Received: 27 February 2018
  •  Accepted: 28 August 2018
  •  Published: 31 October 2018

Abstract

A new block method of order five for the numerical solution of initial value problems is derived. The coefficients of the matrix of the method are chosen such that low power of the blocksize appears in the principal local truncation error. The stability polynomial is shown to be a perturbation of   order explicit Runge-Kutta method.

Key words: Predictor-corrector methods, ordinary differential equations, block methods.