{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:44:10Z","timestamp":1760402650283,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,20]],"date-time":"2020-04-20T00:00:00Z","timestamp":1587340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this work, we present a novel strategy for the numerical solution of a coupled system of partial differential equations that describe reaction\u2013diffusion processes of a mixture of metals and ligands that can be absorbed by a sensor or a microorganism, in an aqueous medium. The novelty introduced in this work consisted of an adequate database management in conjunction with a direct iterative schema, which allowed the construction of simple, fast and efficient algorithms. Except in really adverse conditions, the calculation is converging and satisfactory solutions were reached. Computing times showed to be better than those obtained with some commercial programs. Although we concentrate on the solution for a particular system (Diffusive Gradients in Thin Films [DGT] sensors), the proposed algorithm does not require major modifications to consider new theoretical or experimental configurations. Since the quality of numerical simulations of reaction\u2013diffusion problems often faces some drawbacks as the values of reaction rate constants increase, some additional effort has been invested in obtaining proper solutions in those cases.<\/jats:p>","DOI":"10.3390\/a13040098","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T03:23:06Z","timestamp":1587439386000},"page":"98","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Numerical Simulation of Non-Linear Models of Reaction\u2014Diffusion for a DGT Sensor"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3885-9518","authenticated-orcid":false,"given":"Joan Cecilia","family":"Aver\u00f3s","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Lleida, 25003 Lleida, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaume Puy","family":"Llorens","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Lleida, 25003 Lleida, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6667-8808","authenticated-orcid":false,"given":"Ramiro","family":"Uribe-Kaffure","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Tolima, 730006299 Ibagu\u00e9, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,20]]},"reference":[{"key":"ref_1","unstructured":"Buffle, J., and Horvai, G. 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Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.aca.2015.04.054","article-title":"Influence of the settling of the resin beads on Diffusive Gradients in Thin Films measurements","volume":"885","author":"Altier","year":"2015","journal-title":"Anal. Chim. Acta"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5317","DOI":"10.1021\/es200610n","article-title":"Contribution of partially labile complexes to the DGT metal flux","volume":"45","author":"Uribe","year":"2011","journal-title":"Environ. Sci. Technol."},{"key":"ref_11","unstructured":"Mitchell, A., and Griffiths, D. (1980). The Finite Difference Method in Partial Differential, John Wiley and Sons."},{"key":"ref_12","unstructured":"Hughes, T.J. (1987). 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Chem."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.aca.2019.01.056","article-title":"Time weighted average concentrations measured with Diffusive Gradients in Thin films (DGT)","volume":"1060","author":"Altier","year":"2019","journal-title":"Anal. Chim. 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