Convection of Physical Quantities of Random Density

We study the random flow, through a thin cylindrical tube, of a physical quantity of random density, in the presence of random sinks and sources. We model convection in terms of the expectations of the flux and density and solve the initial value problem for the resulting convection equation. We pro...

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Bibliographic Details
Published in:AppliedMath 2024-03, Vol.4 (1), p.225-249
Main Authors: Barletta, Elisabetta, Dragomir, Sorin, Esposito, Francesco
Format: Article
Language:English
Subjects:
Bochner integral reminder
convection equation
finite-difference approximation schemes
stochastic differential equations
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Summary:We study the random flow, through a thin cylindrical tube, of a physical quantity of random density, in the presence of random sinks and sources. We model convection in terms of the expectations of the flux and density and solve the initial value problem for the resulting convection equation. We propose a difference scheme for the convection equation, that is both stable and satisfies the Courant–Friedrichs–Lewy test, and estimate the difference between the exact and approximate solutions.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath4010012