著者
齊藤 宣一
出版者
一般社団法人 日本応用数理学会
雑誌
応用数理 (ISSN:24321982)
巻号頁・発行日
vol.19, no.4, pp.281-290, 2009-12-24 (Released:2017-04-08)
参考文献数
15

We are concerned with numerical methods for the Keller-Segel system that describes the aggregation of slime molds resulting from their chemotactic features. Whereas the system has positivity and mass conservation properties, it is not certain that numerical schemes for the system preserve these conservation properties. In the present article, we review two conservative numerical schemes proposed by the author and discuss how to choose the time increments and the space meshes in order to realize those conservation properties. The first one is the finite-difference method that makes use of the semi-implicit time discretization with the time-increment control and the upwind difference approximation. The second is the finite-element method that is an application of Baba-Tabata's conservative upwind finite element. Conservative properties are proved via the theory of M-matrices. Error analysis of the finite-element scheme is also summarized. In particular, we have error estimates with explicit convergence rates by virtue of the analytical semigroup theory.

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離散化は斉藤氏のものを採用しました。この文献にはスキームの数学解析も載っており(こちらがメイン)非常に参考になります。 https://t.co/zihsfGSSsD
本文です。 齊藤宣一『Keller-Segel方程式の数値解析』 https://t.co/zihsfGSSsD

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