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Videos Year : 2016

Simulation of the growth-fragmentation equation in a periodic case - Non-dissipative numerical scheme

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Abstract

This video illustrates the study by E. Bernard, M. Doumic and P. Gabriel https://hal.archives-ouvertes.fr/hal-01363549/document by showing the time behaviour of the solution to the following growth-fragmentation equation: $$\frac{\partial}{\partial t} u(t,x) + \frac{\partial}{\partial t} (x u(t,x)) + B(x)u(t,x)=4B(2x)u(t,2x),\qquad u(0,x)=u^{in}(x).$$ The numerical scheme is explicit, and uses a splitting between the transport operator and the fragmentation operator, on a geometric grid. This allows to capture the asymptotic periodic behaviour (due to a lack of dissipativity in the equation).

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medihal-01407826 , version 1 (02-12-2016)

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  • HAL Id : medihal-01407826 , version 1

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Marie Doumic. Simulation of the growth-fragmentation equation in a periodic case - Non-dissipative numerical scheme. 2016. ⟨medihal-01407826⟩

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