Nonstandard Finite Difference Scheme for a Computer Virus Model

Kocabiyik, Mehmet; ÖZDOĞAN, Nihal; Ongun, Mevlüde Yakit

doi:10.38088/jise.705728

Cited by 6 publications

(4 citation statements)

References 37 publications

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“…is related to ℎ step size and 𝑑 variable which can be obtained with the help of equilibrium point. This scheme can be defined in the same way in fractional order differential equations with the help of the approximate Grünwald-Letnikov derivative formula [27][28][29][30][31][32][33][34][35][36]. Resource suggestions for different numerical methods and approaches are as follows [37][38][39][40].…”

Section: Preliminariesmentioning

confidence: 99%

Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Kocabiyik

Ongun

2023

Gazi University Journal of Science

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Estimating effects of drugs at different stages is directly proportional to the duration of recovery and duration of pulling through with the disease. For this reason, solving Pharmacokinetic models that investigate these effects is very important. In this study, numerical solutions of this type of one, two and three compartment nonlinear Pharmacokinetic models have been studied. Distributed order differential equations are used for the solution of the model. Numerical solutions have been found with the density function contained in distributed order differential equations and different values of this function. A Nonstandard finite difference scheme has been used for numerical solutions. Finally, stability analysis of equilibrium points of obtained discretized system has also been expressed with the help of the Schur-Cohn criteria.

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Section: Preliminariesmentioning

confidence: 99%

Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Kocabiyik

Ongun

2023

Gazi University Journal of Science

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“…The phase portrait drawn using NSFD is compatible with the phase portrait drawn using RK4 (Runge-Kutta 4th order method). As in [33,34] it was seen that this method gives accurate and convergence results for very small h. In all calculations with NSFD, the denominator function is selected as ℎ 1 = 𝜑𝜑(ℎ) = (𝑒𝑒 𝛼𝛼 0 ℎ − 1)/𝛼𝛼 0 and ℎ = 0.01 2. Effect of time step sizes on the numerical methods for 𝐸𝐸 0 = 0.004…”

Section: Numerical Simulationsmentioning

confidence: 99%

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

ÖZDOĞAN

Ongun

2022

Journal of Universal Mathematics

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In this paper, we introduced nonstandard finite difference scheme (NSFD) for solving the continuos model with Michaelis-Menten harvesting rate. We have seen that the proposed scheme preserve local stability and positivity. Stability analysis of each fixed point of the discrete time model has been proven. Also, numerical comparisons were made between the nonstandard finite difference method and the other methods.

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“…Numerical calculations are given to support the theoretical study. 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.…”

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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Nonstandard Finite Difference Scheme for a Computer Virus Model

Cited by 6 publications

References 37 publications

Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

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

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

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