{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:50:36Z","timestamp":1760143836605,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,4]],"date-time":"2024-03-04T00:00:00Z","timestamp":1709510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>We systematically investigate the performance of numerical methods to solve Fisher\u2019s equation, which contains a linear diffusion term and a nonlinear logistic term. The usual explicit finite difference algorithms are only conditionally stable for this equation, and they can yield concentrations below zero or above one, even if they are stable. Here, we collect the stable and explicit algorithms, most of which we invented recently. All of them are unconditionally dynamically consistent for Fisher\u2019s equation; thus, the concentration remains in the unit interval for arbitrary parameters. We perform tests in the cases of 1D and 2D systems to explore how the errors depend on the coefficient of the nonlinear term, the stiffness ratio, and the anisotropy of the system. We also measure running times and recommend which algorithms should be used in specific circumstances.<\/jats:p>","DOI":"10.3390\/computation12030049","type":"journal-article","created":{"date-parts":[[2024,3,4]],"date-time":"2024-03-04T10:11:57Z","timestamp":1709547117000},"page":"49","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Systematic Investigation of the Explicit, Dynamically Consistent Methods for Fisher\u2019s Equation"],"prefix":"10.3390","volume":"12","author":[{"given":"Husniddin","family":"Khayrullaev","sequence":"first","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1108-0099","authenticated-orcid":false,"given":"Issa","family":"Omle","sequence":"additional","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"},{"name":"Department of Fluid and Heat Engineering, University of Miskolc, 3515 Miskolc, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0439-3070","authenticated-orcid":false,"given":"Endre","family":"Kov\u00e1cs","sequence":"additional","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1007\/s00285-020-01547-1","article-title":"Travelling wave solutions in a negative nonlinear diffusion\u2013reaction model","volume":"81","author":"Li","year":"2020","journal-title":"J. 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