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

Authors

DOI:

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

Keywords:

Non-local partial differential equations, Social potential, Finite volume method, Non-linear diffusion

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.

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Published

2022-03-07

Issue

Vol. 62 (2020)

Section

Proceedings Computational Techniques and Applications Conference