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dc.contributor.authorBIGERELLE, maxence
dc.contributor.authorIOST, Alain
dc.date.accessioned2015
dc.date.available2015
dc.date.issued2004
dc.date.submitted2015
dc.identifier.urihttp://hdl.handle.net/10985/9816
dc.description.abstractThe aim of this paper is to analyze the physical meaning of the numerical instabilities of the parabolic partial differential equations when solved by finite differences. Even though the explicit scheme used to solve the equations is physically well posed, mathematical instabilities can occur as a consequence of the iteration errors if the discretisation space and the discretisation time satisfy the stability criterion. To analyze the physical meaning of these instabilities, the system is divided in sub-systems on which a Brownian motion takes place. The Brownian motion has on average some mathematical properties that can be analytically solved using a simple diffusion equation. Thanks to this mesoscopic discretisation, we could prove that for each half sub-cell the equality stability criterion corresponds to an inversion of the particle flux and a decrease in the cell entropy in keeping with time as criterion increases. As a consequence, all stability criteria defined in literature can be used to define a physical continuous 'time-length' frontier on which mesoscopic and microscopic models join.
dc.language.isoen
dc.publisherFreund Publishing House Ltd.
dc.rightsPost-print
dc.subjectDiffusion
dc.subjectPartial Differential Equations
dc.subjectFinite Difference Method
dc.subjectStability
dc.subjectfractal
dc.subjectMonte Carlo
dc.titlePhysical Interpretations of the Numerical Instabilities in Diffusion Equations Via Statistical Thermodynamics
dc.typdocArticles dans des revues avec comité de lecture
dc.localisationCentre de Lille
dc.subject.halMathématique: Théorie de l'information et codage
ensam.audienceInternationale
ensam.page121-134
ensam.journalInternational Journal of Nonlinear Sciences and Numerical Simulation
ensam.volume5
ensam.issue2


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