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Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations

Hui Huang Tsinghua University Jian-Guo Liu Duke University

Analysis of PDEs mathscidoc:1702.03020

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES B, 21, (10), 3463 - 3478, 2016.11
In this paper, we discuss error estimates associated with three different aggregation-diffusion splitting schemes for the Keller-Segel equations. We start with one algorithm based on the Trotter product formula, and we show that the convergence rate is CΔt, where Δt is the time-step size. Secondly, we prove the convergence rate CΔt2 for the Strang's splitting. Lastly, we study a splitting scheme with the linear transport approximation, and prove the convergence rate CΔt.
Newtonian aggregation, chemotaxis, random particle method, positivity preserving.
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@inproceedings{hui2016error,
  title={Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations},
  author={Hui Huang, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207205421785799261},
  booktitle={DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES B},
  volume={21},
  number={10},
  pages={3463 - 3478},
  year={2016},
}
Hui Huang, and Jian-Guo Liu. Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations. 2016. Vol. 21. In DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES B. pp.3463 - 3478. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207205421785799261.
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