{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:56:43Z","timestamp":1760057803697,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T00:00:00Z","timestamp":1740528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a robust finite difference method on a fitted Shishkin mesh to solve a system of n singularly perturbed convection\u2013reaction\u2013diffusion differential equations with two small parameters. Defined on the interval [0,1], this system exhibits boundary layers due to the presence of small parameters, making accurate numerical approximations challenging. The method employs a piecewise uniform Shishkin mesh that adapts to layer regions and efficiently captures the solution\u2019s behavior. The scheme is proven to be uniformly convergent with respect to the perturbation parameters, achieving nearly first-order accuracy. Comprehensive numerical experiments validate the theoretical results, illustrating the method\u2019s robustness and efficiency in handling parameter-sensitive boundary layers.<\/jats:p>","DOI":"10.3390\/axioms14030171","type":"journal-article","created":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T11:22:12Z","timestamp":1740568932000},"page":"171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Advanced Fitted Mesh Finite Difference Strategies for Solving \u2018n\u2019 Two-Parameter Singularly Perturbed Convection\u2013Diffusion System"],"prefix":"10.3390","volume":"14","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"}]},{"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0477-1895","authenticated-orcid":false,"given":"George E.","family":"Chatzarakis","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, 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, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,26]]},"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. Therm. Anal. Calorim."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1023\/A:1023631706975","article-title":"Asymptotic analysis and solution of a finite-horizon H\u221e control problem for singularly-perturbed linear systems with small state delay","volume":"117","author":"Glizer","year":"2003","journal-title":"J. Optim. 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Math."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Arthur, J., Chatzarakis, G.E., Panetsos, S.L., and Mathiyazhagan, J.P. (2025). A robust-fitted-mesh-based finite difference approach for solving a system of singularly perturbed convection\u2013diffusion delay differential equations with two parameters. Symmetry, 17.","DOI":"10.20944\/preprints202502.0851.v1"},{"key":"ref_16","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_17","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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