Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations

Ahmad, Nur Amirah; Senu, Norazak; İbrahim, Zarina Bibi; Othman, Mazliza

doi:10.47836/mjms.16.2.04

Cited by 3 publications

(2 citation statements)

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“…The use of stability analysis is required to have information on both the stability of solutions to differential equations and the stability of dynamical systems. Several novel and significant advances have been made in stability analysis and analytical solutions for differential equations (see, for example, but not limited to, [3,20,21]).…”

Section: Introductionmentioning

confidence: 99%

Untitled

2023

MJMS

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In this work, we are interested in studying variations in plasma glucose and insulin levels over time using a fractional-order version of a mathematical model. Applying the fractional-order Caputo derivative, we can investigate different concentration rates among insulin, glucose, and healthy β-cells. The main aim is to obtain the numerical solution of the proposed model in order to show variations in plasma glucose and insulin levels over time, by applying the generalized Euler method. The local stability analysis of the proposed (discretization) Caputo fractionalorder model was discussed. To check the feasibility of our analysis, we have investigated some numerical simulations for various fractional orders by varying values of the parameters with help of Mathematica. Numerical simulations were in good agreement with the theoretical findings. Three specific numerical examples are given as applications of the main results.

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Section: Introductionmentioning

confidence: 99%

Untitled

2023

MJMS

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Section: Introductionmentioning

confidence: 99%

On the Solution of a Nonlinear Fractional-Order Glucose-Insulin System Incorporating β -cells Compartment

Ahmad

2023

MJMS

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In this work, we are interested in studying variations in plasma glucose and insulin levels over time using a fractional-order version of a mathematical model. Applying the fractional-order Caputo derivative, we can investigate different concentration rates among insulin, glucose, and healthy β-cells. The main aim is to obtain the numerical solution of the proposed model in order to show variations in plasma glucose and insulin levels over time, by applying the generalized Euler method. The local stability analysis of the proposed (discretization) Caputo fractional-order model was discussed. To check the feasibility of our analysis, we have investigated some numerical simulations for various fractional orders by varying values of the parameters with help of Mathematica. Numerical simulations were in good agreement with the theoretical findings. Three specific numerical examples are given as applications of the main results.

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A Fractional Order SITR Model for Forecasting of Transmission of COVID-19: Sensitivity Statistical Analysis

Al‐Zahrani¹,

Elsmih²,

Al-Zahrani³

et al. 2022

MJMS

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In this work, we investigate the effects of the contact rate between people on the covid-19 virus transmission through a susceptible-infected-treatment-recovered (SITR) fractional mathematical model. Several strategies are introduced, and the development methodology is constructed up in various cases based on the rate of individual contact, due to confinement and social distancing rules, which can be useful in reducing infection. The existence and uniqueness of the proposed model solution are established, as well as the basic reproduction number. The basic reproduction number has been used to control the dynamics of the fractional SITR model completely, which determines whether or not the infection is extinguished. The global stability of the infection-free balance and endemic equilibrium point of the proposed model has been fully established using the Lyapunov-LaSalle type theorem. Furthermore, a sensitivity analysis is carried out to find out which parameter is the most dominant to affect the disease's endemicity and to see how changes in parameters affect Covid-19's beginning disease transmission. The fractional Adams-Bashforth method is used to compute an iterative solution to the model. Finally, using the model parameter values to explain the importance of the arbitrary fractional-order derivative, the numerical results using MATLAB are presented.

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Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations

Cited by 3 publications

References 20 publications

Untitled

Untitled

On the Solution of a Nonlinear Fractional-Order Glucose-Insulin System Incorporating β -cells Compartment

A Fractional Order SITR Model for Forecasting of Transmission of COVID-19: Sensitivity Statistical Analysis

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