A numerical method for discrete fractional--order chemostat model derived from nonstandard numerical scheme

Document Type: Research Paper

Authors

Department of Mathematics‎, ‎School of Mathematical Sciences‎, ‎Vali-e-Asr University of Rafsanjan‎, ‎Rafsanjan‎, ‎Iran.

Abstract

‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and fourth order Runge--Kutta methods‎. ‎Numerical results show that the NSFD approach is easy and accurate when applied to fractional--order chemostat model.

Keywords

Main Subjects


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Volume 43, Issue 5
September and October 2017
Pages 1165-1182
  • Receive Date: 06 September 2015
  • Revise Date: 24 February 2016
  • Accept Date: 11 May 2016