{"id":"https://openalex.org/W4406026162","doi":"https://doi.org/10.3390/sym17010068","title":"A Robust-Fitted-Mesh-Based Finite Difference Approach for Solving a System of Singularly Perturbed Convection\u2013Diffusion Delay Differential Equations with Two Parameters","display_name":"A Robust-Fitted-Mesh-Based Finite Difference Approach for Solving a System of Singularly Perturbed Convection\u2013Diffusion Delay Differential Equations with Two Parameters","publication_year":2025,"publication_date":"2025-01-03","ids":{"openalex":"https://openalex.org/W4406026162","doi":"https://doi.org/10.3390/sym17010068"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010068","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010068","pdf_url":"https://www.mdpi.com/2073-8994/17/1/68/pdf?version=1735911600","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/1/68/pdf?version=1735911600","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jenolin Arthur","orcid":"https://orcid.org/0009-0006-7756-4957"},"institutions":[{"id":"https://openalex.org/I4076070","display_name":"Bharathidasan University","ror":"https://ror.org/02w7vnb60","country_code":"IN","type":"education","lineage":["https://openalex.org/I4076070"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jenolin Arthur","raw_affiliation_strings":["PG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Trichy 620 017, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0009-0006-7756-4957","affiliations":[{"raw_affiliation_string":"PG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Trichy 620 017, Tamil Nadu, India","institution_ids":["https://openalex.org/I4076070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014915773","display_name":"George E. Chatzarakis","orcid":"https://orcid.org/0000-0002-0477-1895"},"institutions":[{"id":"https://openalex.org/I254421610","display_name":"School of Pedagogical and Technological Education","ror":"https://ror.org/04v3r9z94","country_code":"GR","type":"education","lineage":["https://openalex.org/I254421610"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"George E. Chatzarakis","raw_affiliation_strings":["Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, Athens, Greece","Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Marousi, 15122 Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, Athens, Greece","institution_ids":["https://openalex.org/I254421610"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Marousi, 15122 Athens, Greece","institution_ids":["https://openalex.org/I254421610"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069795166","display_name":"S. L. Panetsos","orcid":"https://orcid.org/0000-0002-4517-0922"},"institutions":[{"id":"https://openalex.org/I254421610","display_name":"School of Pedagogical and Technological Education","ror":"https://ror.org/04v3r9z94","country_code":"GR","type":"education","lineage":["https://openalex.org/I254421610"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"S. L. Panetsos","raw_affiliation_strings":["Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, Athens, Greece","Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Marousi, 15122 Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, Athens, Greece","institution_ids":["https://openalex.org/I254421610"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Marousi, 15122 Athens, Greece","institution_ids":["https://openalex.org/I254421610"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075553239","display_name":"Joseph Paramasivam Mathiyazhagan","orcid":"https://orcid.org/0000-0002-0122-8483"},"institutions":[{"id":"https://openalex.org/I4076070","display_name":"Bharathidasan University","ror":"https://ror.org/02w7vnb60","country_code":"IN","type":"education","lineage":["https://openalex.org/I4076070"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Joseph Paramasivam Mathiyazhagan","raw_affiliation_strings":["PG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Trichy 620 017, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0002-0122-8483","affiliations":[{"raw_affiliation_string":"PG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Trichy 620 017, Tamil Nadu, India","institution_ids":["https://openalex.org/I4076070"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014915773"],"corresponding_institution_ids":["https://openalex.org/I254421610"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00549451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"1","first_page":"68","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.5612357258796692},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5229571461677551},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5197895765304565},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.49852466583251953},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49007999897003174},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.48734602332115173},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.48304539918899536},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4411361813545227},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3964603841304779},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37973907589912415},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36866050958633423},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3205539584159851},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26846057176589966},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24582332372665405},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.15937602519989014},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.06284913420677185}],"concepts":[{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.5612357258796692},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5229571461677551},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5197895765304565},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.49852466583251953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49007999897003174},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.48734602332115173},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48304539918899536},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4411361813545227},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3964603841304779},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37973907589912415},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36866050958633423},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3205539584159851},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26846057176589966},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24582332372665405},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.15937602519989014},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.06284913420677185},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17010068","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010068","pdf_url":"https://www.mdpi.com/2073-8994/17/1/68/pdf?version=1735911600","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0fad8859ae3f4c50ae54e90522a99e48","is_oa":false,"landing_page_url":"https://doaj.org/article/0fad8859ae3f4c50ae54e90522a99e48","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 17, Iss 1, p 68 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym17010068","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010068","pdf_url":"https://www.mdpi.com/2073-8994/17/1/68/pdf?version=1735911600","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406026162.pdf","grobid_xml":"https://content.openalex.org/works/W4406026162.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W67460923","https://openalex.org/W170534876","https://openalex.org/W1476132770","https://openalex.org/W1480673526","https://openalex.org/W1991968181","https://openalex.org/W2036371403","https://openalex.org/W2065770866","https://openalex.org/W2096162628","https://openalex.org/W2139322509","https://openalex.org/W2942981489","https://openalex.org/W2948654771","https://openalex.org/W3087466423","https://openalex.org/W4212955198","https://openalex.org/W4225132399","https://openalex.org/W4394656540","https://openalex.org/W7033887206"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W2171402820","https://openalex.org/W4251142058","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W1965041963","https://openalex.org/W2007426143","https://openalex.org/W2384221708"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,12,30],"robust":[4],"fitted":[5],"mesh":[6,34],"finite":[7],"difference":[8],"method":[9,28],"for":[10,100],"solving":[11],"dynamical":[13],"system":[14],"of":[15],"two":[16],"parameter":[17],"convection\u2013reaction\u2013diffusion":[18],"delay":[19,47],"differential":[20],"equations":[21],"defined":[22],"on":[23],"the":[24,38,69,91,94,101],"interval":[25],"[0,2].":[26],"The":[27,49,84],"incorporates":[29],"piecewise":[31],"uniform":[32],"Shishkin":[33],"to":[35,55,67,75],"accurately":[36],"resolve":[37],"solution":[39],"behavior":[40],"caused":[41],"by":[42,87],"small":[43],"perturbation":[44],"parameters":[45],"and":[46,58,78,96],"terms.":[48],"proposed":[50],"numerical":[51],"scheme":[52],"is":[53],"proven":[54],"be":[56],"parameter-robust":[57],"achieves":[59],"almost":[60],"first-order":[61],"convergence.":[62],"Numerical":[63],"illustrations":[64],"are":[65],"provided":[66],"showcase":[68],"method\u2019s":[70],"effectiveness,":[71],"highlighting":[72],"its":[73],"capability":[74],"address":[76],"boundary":[77],"interior":[79],"layers":[80],"with":[81],"improved":[82],"accuracy.":[83],"results,":[85],"supported":[86],"symmetrical":[88],"considerations":[89],"in":[90],"figures,":[92],"enhance":[93],"precision":[95],"serve":[97],"as":[98],"validation":[99],"theoretical":[102],"results.":[103]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
