Stability Analysis of Discretized Model of Glucose–Insulin Homeostasis

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Turhan Çetinkaya İ., Kocabıyık M., Yakıt Ongun M.

Celal Bayar University Journal of Science, vol.17, no.4, pp.369-377, 2021 (Peer-Reviewed Journal)

• Publication Type: Article / Article
• Volume: 17 Issue: 4
• Publication Date: 2021
• Doi Number: 10.18466/cbayarfbe.838451
• Journal Name: Celal Bayar University Journal of Science
• Journal Indexes: TR DİZİN (ULAKBİM)
• Page Numbers: pp.369-377
• Süleyman Demirel University Affiliated: Yes

Abstract

In this paper, the mathematical model which describes the glucose-insulin homeostasis in healthy rats is considered. The model is discretized by constructing a nonstandard finite difference (NSFD) scheme to obtain the numerical solutions. The equilibrium point of the discretized model is determined and stability analysis of the discretized model is discussed. The effect of time step sizes on 4th order Runge-Kutta method and NSFD method is presented. Also, comparison of NSFD scheme solution, Runge-KuttaFehlberg Method (RKF45) solution and analytical solution are presented in graphical form. The effectiveness of the proposed method in the solution and interpretation of the model is observed.