{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:33:16Z","timestamp":1759969996649,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T00:00:00Z","timestamp":1735862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a robust fitted mesh finite difference method for solving a dynamical system of two parameter convection\u2013reaction\u2013diffusion delay differential equations defined on the interval [0,2]. The method incorporates a piecewise uniform Shishkin mesh to accurately resolve the solution behavior caused by small perturbation parameters and delay terms. The proposed numerical scheme is proven to be parameter-robust and achieves almost first-order convergence. Numerical illustrations are provided to showcase the method\u2019s effectiveness, highlighting its capability to address boundary and interior layers with improved accuracy. The results, supported by symmetrical considerations in the figures, enhance the precision and serve as validation for the theoretical results.<\/jats:p>","DOI":"10.3390\/sym17010068","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T10:17:23Z","timestamp":1735899443000},"page":"68","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Robust-Fitted-Mesh-Based Finite Difference Approach for Solving a System of Singularly Perturbed Convection\u2013Diffusion Delay Differential Equations with Two Parameters"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-7756-4957","authenticated-orcid":false,"given":"Jenolin","family":"Arthur","sequence":"first","affiliation":[{"name":"PG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Trichy 620 017, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"George E.","family":"Chatzarakis","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. L.","family":"Panetsos","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0122-8483","authenticated-orcid":false,"given":"Joseph Paramasivam","family":"Mathiyazhagan","sequence":"additional","affiliation":[{"name":"PG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Trichy 620 017, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2259","DOI":"10.1007\/s10973-020-10233-9","article-title":"Intra-uterine particle-fluid motion through a compliant asymmetric tapered channel with heat transfer","volume":"144","author":"Bhatti","year":"2021","journal-title":"J. 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Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1080\/0020716042000301798","article-title":"Parameter-uniform finite difference scheme for a system of coupled singularly perturbed convection-diffusion equations","volume":"82","author":"Cen","year":"2005","journal-title":"Int. J. Comput. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1016\/j.apnum.2005.08.002","article-title":"A parameter robust second order numerical method for a singularly perturbed two-parameter problem","volume":"56","author":"Gracia","year":"2006","journal-title":"Appl. Numer. 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Symmetry, 11.","DOI":"10.3390\/sym11050628"},{"key":"ref_13","first-page":"587","article-title":"Second order parameter-uniform convergence for a finite difference method for a singularly perturbed linear reaction-diffusion system","volume":"15","author":"Mathiyazhagan","year":"2010","journal-title":"Math. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"424","DOI":"10.2478\/cmam-2003-0028","article-title":"Singularly perturbed problems modeling reaction-convection-diffusion processes","volume":"3","author":"Pickett","year":"2003","journal-title":"Comput. Methods Appl. Math."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Farrell, P., Hegarty, A., Miller, J.M., O\u2019Riordan, E., and Shishkin, G.I. (2000). Robust Computational Techniques for Boundary Layers, Chapman and Hall\/CRC. 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