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Hyperbolic and Kinetic Models for Self-organised Biological Aggregations pp 195–226Cite as

Numerical Approaches for Kinetic and Hyperbolic Models

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Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2232))

Abstract

Due to the complexity of hyperbolic and kinetic models discussed in the previous chapters, it is difficult to gain much understanding of the behaviour of the models only from analytical results. As we have already seen throughout this study, numerical approaches are critical when trying to unravel the patterns exhibited by these models. There are a large variety of approaches to discretise and simulate numerically the kinetic and hyperbolic models described in the previous sections. However, due to the intense activity of this field, it is impossible to do a detailed review of all numerical schemes developed over the past 50–60 years. Therefore, in this chapter we briefly discuss some of these approaches, to give the reader a glimpse of the large variety of numerical schemes existent in the literature. We start by discussing a few numerical methods for macroscopic hyperbolic models, followed by a discussion on the numerical methods for more complex (and higher dimension) kinetic equations. We conclude this chapter with a brief overview of different boundary conditions.

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  1. Division of Mathematics, University of Dundee, Dundee, UK

    Raluca Eftimie

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  1. Raluca Eftimie
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Eftimie, R. (2018). Numerical Approaches for Kinetic and Hyperbolic Models. In: Hyperbolic and Kinetic Models for Self-organised Biological Aggregations. Lecture Notes in Mathematics(), vol 2232. Springer, Cham. https://doi.org/10.1007/978-3-030-02586-1_7

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