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 mentioned fractional system, the well known nonstandard nite dierence (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.
In this paper, numerical solution of the generalized Burgers‐Fisher (BF) equation is presented on the basis of the nonstandard finite‐difference (NSFD) scheme. At first, two exact finite‐difference schemes for the BF equation are obtained. Afterwards, an NSFD scheme is presented for this equation. The positivity, consistency, and boundedness of the scheme are discussed. The numerical results obtained by the NSFD scheme is compared with the exact solution and some available methods to verify the accuracy and efficiency of the NSFD scheme.
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