Nonstandard finite difference scheme for a Tacoma Narrows Bridge model

Adekanye, Oluwaseye; Washington, Talitha M.

doi:10.1016/j.apm.2018.05.027

Cited by 47 publications

(31 citation statements)

References 12 publications

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“…Motivated by this, we will investigate the complete global stability of model (1) in this work. More precisely, we will prove the following result on the global stability of the DEE point of model (1).…”

Section: Introductionmentioning

confidence: 99%

“…Many real-life problems are usually best described by differential equations and, in general, it is impossible to find exact solutions to these differential equations. In particular, it is also impossible to find an exact solution to model (1). Therefore, our next objective is to consider effective numerical schemes for solving model (1).…”

Section: Introductionmentioning

confidence: 99%

“…In particular, it is also impossible to find an exact solution to model (1). Therefore, our next objective is to consider effective numerical schemes for solving model (1). It should be emphasized that numerical schemes for solving model (1) have not been considered in the previous work [26].…”

Section: Introductionmentioning

confidence: 99%

“…In Sect. 2, we investigate the global stability of model (1). NSFD schemes are constructed and analyzed in Sect.…”

Section: Introductionmentioning

confidence: 99%

“…2 Global stability of model (1) In this section, the global stability of model (1) is re-established. Note that the first and the second equations of model (1) only include the components S and I.…”

Section: Introductionmentioning

confidence: 99%

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On the global asymptotic stability of a hepatitis B epidemic model and its solutions by nonstandard numerical schemes

Hoang

Egbelowo

2020

Bol. Soc. Mat. Mex.

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Very recently, a hepatitis B epidemic model with saturated incidence rate has been proposed and analyzed in Khan et al. (Chaos Solitons Fractals 124:1-9, 2019). The local asymptotic stability of the disease endemic equilibrium (DEE) point of model has been established theoretically but its global asymptotic stability has not been studied. In this paper, we present a mathematically rigorous analysis for the global asymptotic stability of the DEE point of the model. More precisely, we prove that if the DEE point exists, then it is not only locally asymptotically stable but also globally asymptotically stable. Furthermore, we present an alternative proof for the global stability of the disease-free equilibrium point. The main result is that we obtain the complete global stability of the hepatitis B virus model. Besides, we construct nonstandard finite difference (NSFD) schemes preserving the essential qualitative properties of the continuous model. These properties include the positivity of solutions and the stability of the model. Dynamical properties of the proposed schemes are rigorously investigated by mathematical analyses and numerical simulations. Finally, numerical simulations are performed to confirm the validity of the theoretical results as well as the advantages of the NSFD schemes. Numerical simulations also indicate that the NSFD schemes are appropriate and effective to solve the continuous model. Meanwhile, the standard finite difference schemes such as the Euler scheme, the classical fourth-order Runge-Kutta scheme cannot preserve the essential properties of the continuous model. Consequently, they can generate numerical approximations which are completely different from the solutions of the model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%