A numerical scheme for non-local aggregation with non-linear diffusion and approximations of social potential

Title: A numerical scheme for non-local aggregation with non-linear diffusion and approximations of social potential
Creator: Georgiou, Fillipe Harry; Lamichhane, Bishnu; Thamwattana, Natalie; Buhl, Jerome; Green, Edward
Relation: ANZIAM Journal Vol. 62, Issue 2022, p. C242-C255
Publisher Link: http://dx.doi.org/10.21914/anziamj.v62.16056
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2022
Description: Aggregations abound in nature, from cell formations to locust swarms. One method of modelling these aggregations is the non-local aggregation equation with the addition of degenerate diffusion. In this article we develop a finite volume based numerical scheme for this style of equation and perform an error, computation time, and convergence analysis. In addition we investigate two methods for approximating the non-local component.
Subject: non-local partial differential equations; social potential; finite volume method; non-linear diffusion
Identifier: http://hdl.handle.net/1959.13/1478461
Identifier: uon:50182
Identifier: ISSN:1446-1811
Language: eng
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