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

Fillipe Harry Georgiou; Bishnu Lamichhane; Natalie Thamwattana; Jerome Buhl; Edward Green

doi:10.21914/anziamj.v62.16056

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

https://doi.org/10.21914/anziamj.v62.16056

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

Mar 7, 2022
ANZIAM Journal
Fillipe Harry Georgiou +4 more

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Abstract

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.