On nonstandard finite difference schemes in biosciences | Zendy

Roumen Anguelov | Zendy; Yves Dumont | Zendy; Jean Lubuma | Zendy

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On nonstandard finite difference schemes in biosciences

Author(s) -

Roumen Anguelov,

Yves Dumont,

Jean Lubuma

Publication year - 2012

Publication title -

aip conference proceedings

Language(s) - English

Resource type - Conference proceedings

SCImago Journal Rank - 0.177

H-Index - 75

eISSN - 1551-7616

pISSN - 0094-243X

DOI - 10.1063/1.4758961

Subject(s) - stability (learning theory) , finite difference , advection , finite difference method , exponential stability , mathematics , property (philosophy) , diffusion , differential equation , computer science , mathematical analysis , physics , nonlinear system , philosophy , epistemology , quantum mechanics , machine learning , thermodynamics

We design, analyze and implement nonstandard finite difference (NSFD) schemes for some differential models in biosciences. The NSFD schemes are reliable in three directions. They are topologically dynamically consistent for onedimensional models. They can replicate the global asymptotic stability of the disease-free equilibrium of the MSEIR model in epidemiology whenever the basic reproduction number is less than 1. They preserve the positivity and boundedness property of solutions of advection-reaction and reaction-diffusion equations.

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