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

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  • 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 $C\Delta t$.
    Mathematics Subject Classification: Primary: 65M12, 65M15; Secondary: 92C17.

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