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It is shown that the numerical schemes yield second-order accuracy in time and fourth-order accuracy in space. Some numerical experiments are demonstrated to verify the accuracy and reliability of the proposed schemes. Furthermore, the blow-up phenomenon and bacterial pattern formation are numerically simulated.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023065","type":"journal-article","created":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T04:45:03Z","timestamp":1688445903000},"page":"1471-1492","source":"Crossref","is-referenced-by-count":0,"title":["High-order finite difference approximation of the Keller-Segel model with additional self- and cross-diffusion terms and a logistic source"],"prefix":"10.3934","volume":"18","author":[{"given":"Panpan","family":"Xu","sequence":"first","affiliation":[{"name":"Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, 750021, China"}]},{"given":"Yongbin","family":"Ge","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, 750021, China"}]},{"given":"Lin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023065-1","doi-asserted-by":"publisher","unstructured":"M. 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