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Their behavior is often illustrated using numerical simulations, which require a spatial discretization. In this paper, we establish that periodic solutions to time-periodic integrodifference equations, their stability and their Floquet spectrum persist under discretization of Nystr\u00f6m-type, which replaces integrals by quadrature or cubature rules. Moreover, it is shown that the convergence rates of the particular integration rules are preserved. By means of a typical model from theoretical ecology, these results are demonstrated in terms of a numerical continuation for periodic solutions and their Floquet multipliers.<\/jats:p>","DOI":"10.1007\/s11075-024-01839-3","type":"journal-article","created":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T10:02:16Z","timestamp":1714125736000},"page":"1429-1465","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Nystr\u00f6m discretization of integrodifference equations: numerical continuation of periodic solutions and Floquet multipliers"],"prefix":"10.1007","volume":"98","author":[{"given":"Christian","family":"P\u00f6tzsche","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Rackl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,4,26]]},"reference":[{"key":"1839_CR1","doi-asserted-by":"crossref","unstructured":"Allgower E., Georg K.: Numerical continuation methods. 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