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A nonstandard finite difference numerical scheme applied to a mathematical model of the prevalence of smoking in Spain: a case study

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Computational and Applied Mathematics : Volume 32

A nonstandard finite difference numerical scheme applied to a mathematical model of the prevalence of smoking in Spain: a case study

Content Provider	Springer Nature Link
Author	Arenas, Abraham J. González Parra, Gilberto Guerrero, Francisco
Copyright Year	2013
Abstract	In the present work, we develop a nonstandard finite difference (NSFD) scheme to numerically solve a mathematical model for smoking habit dynamics. The model is described by a system of nonlinear ordinary differential equations, the solution of which predicts the evolution of the prevalence of smoking in Spain. This model has been successfully used to quantify the impact of the Spanish smoke-free law of 2006. According to the principles of dynamic consistency, we constructed an NSFD scheme to integrate numerically the smoking model. This NSFD scheme preserves the properties of the solution corresponding to the original continuous mathematical model such as positivity, local stability of equilibrium points and the associated conservation law. We performed some numerical comparisons with Euler, trapezoidal and fourth-order Runge–Kutta methods to test the NSFD scheme and corroborate that it is dynamically consistent. It is concluded that the NSFD scheme is well suited to numerically solve the mathematical model for smoking habit dynamics.
Starting Page	13
Ending Page	25
Page Count	13
File Format	PDF
ISSN	01018205
Journal	Computational and Applied Mathematics
Volume Number	33
Issue Number	1
e-ISSN	18070302
Language	English
Publisher	Springer Basel
Publisher Date	2013-05-29
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonstandard finite difference Tobacco Computational Mathematics and Numerical Analysis Stability Mathematical Applications in Computer Science Positivity Initial value problems Applications of Mathematics Mathematical Applications in the Physical Sciences Finite difference methods
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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