A linear population model for diabetes mellitus

Vanitha, R; Porchelvi, R Sophia

doi:10.5958/2320-3226.2017.00033.9

Cited by 1 publication

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“…Stability analysis is given. Furthermore, Vanitha and Porchelvi [6] consider the linear mathematical model of diabetes mellitus. A numerical solution by the Euler-Cauchy method is presented.…”

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

View full text Add to dashboard Cite

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A linear population model for diabetes mellitus

Cited by 1 publication

References 0 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

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