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Yaghoubi, Abdulrahman, Saberi Najafi, Hashem. (1400). Numerical solution of the SIR epidemic model using the non-standard finite difference method. , 7(33), 153-164.
Abdulrahman Yaghoubi; Hashem Saberi Najafi. "Numerical solution of the SIR epidemic model using the non-standard finite difference method". , 7, 33, 1400, 153-164.
Yaghoubi, Abdulrahman, Saberi Najafi, Hashem. (1400). 'Numerical solution of the SIR epidemic model using the non-standard finite difference method', , 7(33), pp. 153-164.
Yaghoubi, Abdulrahman, Saberi Najafi, Hashem. Numerical solution of the SIR epidemic model using the non-standard finite difference method. , 1400; 7(33): 153-164.

Numerical solution of the SIR epidemic model using the non-standard finite difference method

Journal of New Researches in Mathematics
مقاله 12، دوره 7، شماره 33، فروردین و اردیبهشت 2022، صفحه 153-164  XML اصل مقاله (322.37 K)
نوع مقاله: research paper
نویسندگان
Abdulrahman Yaghoubi1؛ Hashem Saberi Najafi email orcid 2
1Department of Applied Mathematics, Saravan Branch, Islamic Azad University, Saravan, Iran.
2Department of Applied Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, Lahijan, Iran.
چکیده
In this paper, a special case of the finite difference method which is called non-standard finite difference method is studied for the numerical solution of a mathematical model of epidemic diseases. The constructed non-standard finite difference schemes have the main properties of the continuous model such as positivity, boundedness, and stability. The stability of the equilibrium points of the system is investigated. The proposed non-standard finite difference schemes are convergent to the equilibrium points of the system. In solving nonlinear problems, one of the important advantages of this method is that nonlinear term discretized with nonlocal approximations. In most cases, non-standard finite difference schemes are stable even when large step sizes are considered. Therefore, using non-standard method will be cost-effective in dynamical systems that are studied over a large time interval. Numerical examples confirm the accuracy and efficiency of the non-standard finite difference method.

Keywords: Non-Standard Finite Difference Method, SIR Model, Equilibrium Points.
کلیدواژه‌ها
Non-Standard Finite Difference Method؛ Stability؛ Equilibrium Points؛ Epidemic Diseases
مراجع

[1] R. E. Mickens, (1994), Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore.

 

[2] R. E. Mickens, (2000), Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore.

 

[3] Ronald E. Mickens‚ (2001), A Nonstandard Finite Difference Scheme for a Nonlinear PDE Having Diffusive Shock Wave Solutions‚ Mathematics and Computers in Simulation. 55, 549-555.

 

[4] Ronald E. Mickens‚ (2003), A Nonstandard Finite Difference Scheme for a Fisher PDE Having Nonlinear Diffusion‚ Diffusion‚ Comput.  Math. Appl. 45, 429-436.

 

[5] R. E. Mickens, (2005), Nonstandard Finite Difference Schemes for Differential Equations, Journal of Difference Equations and Applications, Vol. 8, No. 9, pp. 823-847

 

[6] Ronald E. Mickens‚ (2005), Advances in the Applications of Nonstandard Finite Difference Schemes, World Scientific‚ Singapore.

 

[7] Ronald E. Mickens‚ (2005), A Nonstandard Finite Difference Scheme for a PDE Modeling Combustion with Nonlinear Advection and Diffusion‚ Mathematics and Computers in Simulation. 69, 439-446.

 

[8] Ronald E. Mickens‚ (2006), Calculation of Denominator Functions for Nonstandard Finite Difference Schemes for Differential Equations Satisfying a Positivity Condition‚ Wiley Inter Science‚ 23 (3), 672-691.   

[9] Ronald E. Mickens‚ (2007), Determination of Denominator Functions for a NSFD Scheme for the Fisher PDE with Linear Advection‚ Mathematics and Computers in Simulation. 74, 190-195.

 

[10] Najafi, H. S., Yaghoubi, A. R.,

(2014), Solving Dynamic Equation by the Non-Standard Finite Difference Method, Journal of Computer Science & Computational Mathematics, 4 (4), 57-60.

 

[11] Yaghoubi, A. R., Najafi, H. S., (2015), Comparison Between Standard and Non-standard Finite Difference Methods for Solving First and Second Order Ordinary Differential Equations, International Journal of Applied Mathematical Research, 4 (2), 316-324.

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