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

作者：Huang, Hui^*; Liu, Jian-Guo

来源：Discrete and Continuous Dynamical Systems-Series B, 2016, 21(10): 3463-3478.

DOI：10.3934/dcdsb.2016107

• Newtonian aggregation
• chemotaxis
• random particle method
• positivity preserving

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.

• 出版日期2016-12
• 单位清华大学