{"id":"https://openalex.org/W4280551565","doi":"https://doi.org/10.3390/sym14051046","title":"Stable Difference Schemes with Interpolation for Delayed One-Dimensional Transport Equation","display_name":"Stable Difference Schemes with Interpolation for Delayed One-Dimensional Transport Equation","publication_year":2022,"publication_date":"2022-05-19","ids":{"openalex":"https://openalex.org/W4280551565","doi":"https://doi.org/10.3390/sym14051046"},"language":"en","primary_location":{"id":"doi:10.3390/sym14051046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051046","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1046/pdf?version=1654499003","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/2073-8994/14/5/1046/pdf?version=1654499003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Karthick Sampath","orcid":"https://orcid.org/0000-0001-5758-4703"},"institutions":[{"id":"https://openalex.org/I145286018","display_name":"SRM Institute of Science and Technology","ror":"https://ror.org/050113w36","country_code":"IN","type":"education","lineage":["https://openalex.org/I145286018"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Karthick Sampath","raw_affiliation_strings":["Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu 603203, India"],"raw_orcid":"https://orcid.org/0000-0001-5758-4703","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu 603203, India","institution_ids":["https://openalex.org/I145286018"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058954608","display_name":"Subburayan Veerasamy","orcid":"https://orcid.org/0000-0003-2102-5322"},"institutions":[{"id":"https://openalex.org/I145286018","display_name":"SRM Institute of Science and Technology","ror":"https://ror.org/050113w36","country_code":"IN","type":"education","lineage":["https://openalex.org/I145286018"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Subburayan Veerasamy","raw_affiliation_strings":["Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu 603203, India"],"raw_orcid":"https://orcid.org/0000-0003-2102-5322","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu 603203, India","institution_ids":["https://openalex.org/I145286018"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055431798","display_name":"Ravi P. Agarwal","orcid":"https://orcid.org/0000-0003-0634-2370"},"institutions":[{"id":"https://openalex.org/I181414168","display_name":"Texas A&M University \u2013 Kingsville","ror":"https://ror.org/05abs3w97","country_code":"US","type":"education","lineage":["https://openalex.org/I181414168"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ravi Agarwal","raw_affiliation_strings":["Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA"],"raw_orcid":"https://orcid.org/0000-0003-0634-2370","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA","institution_ids":["https://openalex.org/I181414168"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055431798","https://openalex.org/A5058954608"],"corresponding_institution_ids":["https://openalex.org/I145286018","https://openalex.org/I181414168"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.9213,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82929219,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"14","issue":"5","first_page":"1046","last_page":"1046"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"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":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/discontinuity","display_name":"Discontinuity (linguistics)","score":0.7627295255661011},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7450997829437256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6889325380325317},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.611853837966919},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5529784560203552},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5427865982055664},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4576486647129059},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4558119475841522},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44353240728378296},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.43831580877304077},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.42450517416000366},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3622484803199768},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19914200901985168}],"concepts":[{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.7627295255661011},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7450997829437256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6889325380325317},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.611853837966919},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5529784560203552},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5427865982055664},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4576486647129059},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4558119475841522},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44353240728378296},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.43831580877304077},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.42450517416000366},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3622484803199768},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19914200901985168},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14051046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051046","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1046/pdf?version=1654499003","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:5c486712150b48cd8d72030e2816ab86","is_oa":true,"landing_page_url":"https://doaj.org/article/5c486712150b48cd8d72030e2816ab86","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 5, p 1046 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/5/1046/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14051046","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14051046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051046","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1046/pdf?version=1654499003","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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4280551565.pdf"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W280536263","https://openalex.org/W1550341792","https://openalex.org/W1635779336","https://openalex.org/W1855169650","https://openalex.org/W1963927951","https://openalex.org/W1982337005","https://openalex.org/W2023386866","https://openalex.org/W2028331352","https://openalex.org/W2029924743","https://openalex.org/W2045781415","https://openalex.org/W2046904024","https://openalex.org/W2052798315","https://openalex.org/W2060410217","https://openalex.org/W2089106221","https://openalex.org/W2129590786","https://openalex.org/W2139670194","https://openalex.org/W2142789340","https://openalex.org/W2226129281","https://openalex.org/W2399287928","https://openalex.org/W2482071863","https://openalex.org/W2604512511","https://openalex.org/W3129412741","https://openalex.org/W3191310976","https://openalex.org/W4206606848","https://openalex.org/W4206906561","https://openalex.org/W4211202937","https://openalex.org/W4229488897","https://openalex.org/W4238975139","https://openalex.org/W6665566036","https://openalex.org/W6679409744","https://openalex.org/W6800317763","https://openalex.org/W6807232350"],"related_works":["https://openalex.org/W2382426030","https://openalex.org/W4303468906","https://openalex.org/W1479673685","https://openalex.org/W2330640442","https://openalex.org/W2069127908","https://openalex.org/W1544816068","https://openalex.org/W2075020252","https://openalex.org/W1975234065","https://openalex.org/W2171402820","https://openalex.org/W4251142058"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"consider":[4],"the":[5,20,27,30,33,42,83,86,94,109],"one-dimensional":[6],"transport":[7],"equation":[8],"with":[9,49,77,100],"delay":[10,72],"and":[11,56,74],"advanced":[12],"arguments.":[13],"A":[14],"maximum":[15,28],"principle":[16],"is":[17,35,38,98],"proven":[18,40],"for":[19,107],"problem":[21],"considered.":[22],"As":[23,80],"an":[24],"application":[25],"of":[26,32,65,85,93],"principle,":[29],"stability":[31],"solution":[34],"established.":[36],"It":[37],"also":[39],"that":[41,52],"solution\u2019s":[43],"discontinuity":[44],"propagates.":[45],"Finite":[46],"difference":[47,87],"methods":[48,69],"linear":[50],"interpolation":[51],"are":[53,59,89,105],"conditionally":[54],"stable":[55,58,67,96],"unconditionally":[57,66],"presented.":[60],"This":[61],"paper":[62],"presents":[63],"applications":[64],"numerical":[68,101],"to":[70],"symmetric":[71],"arguments":[73],"differential":[75],"equations":[76],"variable":[78],"delays.":[79],"a":[81],"consequence,":[82],"matrices":[84],"schemes":[88],"asymmetric.":[90],"An":[91],"illustration":[92],"unconditional":[95],"method":[97],"provided":[99],"examples.":[102],"Solution":[103],"graphs":[104],"drawn":[106],"all":[108],"problems.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
