{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:42:28Z","timestamp":1760146948678,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,26]],"date-time":"2024-12-26T00:00:00Z","timestamp":1735171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Algerian Ministry of Higher Education and Scientific Research","award":["C00L03UN340120230004"],"award-info":[{"award-number":["C00L03UN340120230004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study addresses the diffusion of oxygen in a spherical geometry with simultaneous absorption at a constant rate. The analytical method assumes a polynomial representation of the oxygen concentration profile, leading to a system of differential equations through mathematical manipulation. A numerical scheme is then employed to solve this system, linking the moving boundary and its velocity to determine the unknown functions within the assumed polynomial. An approximate analytical solution is obtained and compared with other methods, demonstrating very good agreement. This approach provides a novel method for addressing oxygen diffusion in spherical geometries, combining analytical techniques with numerical computations to efficiently solve for oxygen concentration profiles and moving boundary dynamics.<\/jats:p>","DOI":"10.3390\/axioms14010004","type":"journal-article","created":{"date-parts":[[2024,12,26]],"date-time":"2024-12-26T21:13:18Z","timestamp":1735247598000},"page":"4","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Solution of Oxygen Diffusion Problem in Spherical Cell"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5844-3603","authenticated-orcid":false,"given":"Soumaya","family":"Belabbes","sequence":"first","affiliation":[{"name":"Laboratory of Fundamental and Numerical Mathematics, Faculty of Sciences, Ferhat Abbas University, S\u00e9tif 19137, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2241-3941","authenticated-orcid":false,"given":"Abdellatif","family":"Boureghda","sequence":"additional","affiliation":[{"name":"Laboratory of Fundamental and Numerical Mathematics, Faculty of Sciences, Ferhat Abbas University, S\u00e9tif 19137, Algeria"},{"name":"Department of Mathematics, IRIMAS, Faculty of Sciences and Techniques, Haute Alsace University, 6 rue des Fr\u00e8res Lumi\u00e8re, 68093 Mulhouse CEDEX, France"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1093\/imamat\/10.1.19","article-title":"A moving boundary problem arising from the diffusion of oxygen in absorbing tissue","volume":"10","author":"Crank","year":"1972","journal-title":"J. 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Free and Moving Boundary Problems, Clarendon Press."},{"key":"ref_9","first-page":"341","article-title":"Solution of an ice melting problem using a fixed domain method with a moving boundary","volume":"62","author":"Boureghda","year":"2019","journal-title":"Bull. Math. Soc. Sci. Math. Roum."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1440","DOI":"10.22436\/jnsa.009.04.04","article-title":"Solution to an ice melting cylindrical problem","volume":"9","author":"Boureghda","year":"2016","journal-title":"J. Nonlinear Sci. Appl. (JNSA)"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1080\/23324309.2023.2271229","article-title":"Du Fort-Frankel Finite Difference Scheme for Solving of Oxygen Diffusion Problem Inside One Cell","volume":"52","author":"Boureghda","year":"2023","journal-title":"J. Comput. Theor. Transp."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1080\/10236198.2011.561797","article-title":"A modified variable time step method for solving ice melting problem","volume":"18","author":"Boureghda","year":"2012","journal-title":"J. Differ. Equ. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.1080\/10255842.2021.2024168","article-title":"A moving boundary model for oxygen diffusion in a sick cell","volume":"25","author":"Djellab","year":"2022","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1002\/cnm.857","article-title":"Numerical solution of the oxygen diffusion in absorbing tissue with a moving boundary","volume":"22","author":"Boureghda","year":"2006","journal-title":"Commun. Numer. Methods Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1108\/09615539910276115","article-title":"An approximate method for oxygen diffusion in a sphere with simultaneous absorption","volume":"9","author":"Ahmed","year":"1999","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/0307-904X(90)90044-6","article-title":"Diffusion of oxygen in a sphere with simultaneous absorption","volume":"14","author":"Gupta","year":"1990","journal-title":"Appl. Math. 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