Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations

Abstract : In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients that are given as averages of solutions to appropriate Poisson equations. We present a new numerical method for computing these coefficients that is based on the calculation of the eigenvalues and eigenfunctions of a Schrodinger operator. These theoretical results are supported by numerical simulations showcasing the efficiency of the method.
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Journal articles
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https://hal.inria.fr/hal-01150161
Contributor : Thierry Goudon <>
Submitted on : Friday, May 8, 2015 - 6:58:17 PM
Last modification on : Tuesday, April 2, 2019 - 2:15:39 PM

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  • HAL Id : hal-01150161, version 1

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Thierry Goudon, Virginie Bonnaillie-Noël, José Antonio Carrillo, Grigorios Pavliotis. Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2016. ⟨hal-01150161⟩

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