ERROR ESTIMATES OF THE AGGREGATION -DIFFUSION SPLITTING ALGORITHMS FOR THE KELLER-SEGEL EQUATIONS

被引：2

作者：

Huang, Hui ^{[1
,2
,3
]}

Liu, Jian-Guo ^{[2
,3
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Duke Univ, Dept Phys, Durham, NC 27708 USA

[3] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2016年 / 21卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Newtonian aggregation; chemotaxis; random particle method; positivity preserving; CONVERGENCE;

D O I：

10.3934/dcdsb.2016107

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 C Delta t, where Delta t is the time-step size. Secondly, we prove the convergence rate C Delta t(2) for the Strang's splitting. Lastly, we study a splitting scheme with the linear transport approximation, and prove the convergence rate C Delta t.

引用

页码：3463 / 3478

页数：16

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