{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:21:10Z","timestamp":1760059270718,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"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>Recently, new and nontrivial analytical solutions that contain the Kummer functions have been found for an equation system of two diffusion\u2013reaction equations. The equations are coupled by two different types of linear reaction terms which have explicit time-dependence. We first make some corrections to these solutions in the case of two different reaction terms. Then, we collect eight efficient explicit numerical schemes which are unconditionally stable if the reaction terms are missing, and apply them to the system of equations. We show that they severely outperform the standard explicit methods when low or medium accuracy is required. Using parameter sweeps, we thoroughly investigate how the performance of the methods depends on the coefficients and parameters such as the length of the examined time interval. We obtained that, similarly to the single-equation case, the leapfrog\u2013hopscotch method is usually the most efficient to solve these problems.<\/jats:p>","DOI":"10.3390\/computation13060129","type":"journal-article","created":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T03:19:38Z","timestamp":1748834378000},"page":"129","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Solution of Coupled Systems of Reaction\u2013Diffusion Equations Using Explicit Numerical Methods with Outstanding Stability Properties"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-4988-8079","authenticated-orcid":false,"given":"Husniddin","family":"Khayrullaev","sequence":"first","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"}]},{"given":"Andicha","family":"Zain","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, 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":[[2025,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jacobs, M.H. 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