Dynamical Behaviours of a Discretized Model With Michaelis-Menten Harvesting Rate

ÖZDOĞAN, Nihal; Ongun, Mevlüde Yakit

doi:10.33773/jum.1134168

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…Dang and Hoang [28], and Kocabıyık et al [29] approximate a computer virus model with the NSFD method. Ozdogan and Ongun [30] solve a mathematical model describing the Michaelis-Menten harvesting rate with the help of NSFD schemes. NSFD discretization of a distributed order smoking model is presented to determine the effects of smoking on humans by Kocabiyik and Ongun [31].…”

Section: Introductionmentioning

confidence: 99%

An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications

TURHAN ÇETİNKAYA

2023

Journal of New Theory

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In this study, a mathematical model describing diabetes mellitus and its complications in a population is considered. Since standard numerical methods can lead to numerical instabilities, it aims to solve the problem using a nonstandard method. Among the nonstandard methods, nonstandard finite difference (NSFD) schemes that satisfy dynamical consistency are preferred to make the model discrete. Both continuous and discrete models are analyzed to show the stability of the model at the equilibrium points. The Schur-Cohn criterion is used to perform stability analysis at the equilibrium point of the discretized model. Thus, asymptotically stability of the model is presented. Moreover, the advantages of the NSFD method are emphasized by comparing the stability for different step sizes with classical methods, such as Euler and Runge-Kutta. It has been observed that the NSFD method is convergence for larger step sizes. In addition, the numerical results obtained by NSFD schemes are compared with the Runge–Kutta–Fehlberg (RKF45) method in graphical forms. The accuracy of the NSFD method is observed.

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Section: Introductionmentioning

confidence: 99%

An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications

TURHAN ÇETİNKAYA

2023

Journal of New Theory

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A Nonstandard Finite Difference Scheme for a Mathematical Model Presenting the Climate Change on the Oxygen-plankton System

Al Jammali,

Turhan Çetinkaya

2024

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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This paper presents a mathematical model describing climate change in the oxygen-plankton system. The model consists of a system of non-linear ordinary differential equations. The Nonstandard Finite Difference (NSFD) method is applied to discretize the non-linear system. The stability of the continuous and discrete model is presented for the given parameters in the literature. The compatibility of the results has been seen. Moreover, the model is solved by both the NSFD method and the Runge–Kutta–Fehlberg (RKF45) method. The numerical results are compared. Furthermore, the efficiency of the NSFD method compared to classical methods such as the Euler method and the fourth order Runge-Kutta (RK4) method for the bigger step size is shown in tabular form.

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Dynamical Behaviours of a Discretized Model With Michaelis-Menten Harvesting Rate

Cited by 2 publications

References 28 publications

An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications

An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications

A Nonstandard Finite Difference Scheme for a Mathematical Model Presenting the Climate Change on the Oxygen-plankton System

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