{"id":"https://openalex.org/W4405928056","doi":"https://doi.org/10.3390/sym17010047","title":"Symmetries of Bernstein Polynomial Differentiation Matrices and Applications to Initial Value Problems","display_name":"Symmetries of Bernstein Polynomial Differentiation Matrices and Applications to Initial Value Problems","publication_year":2024,"publication_date":"2024-12-30","ids":{"openalex":"https://openalex.org/W4405928056","doi":"https://doi.org/10.3390/sym17010047"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010047","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010047","pdf_url":"https://www.mdpi.com/2073-8994/17/1/47/pdf?version=1735558015","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/2073-8994/17/1/47/pdf?version=1735558015","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056432133","display_name":"Nikola Mirkov","orcid":"https://orcid.org/0000-0002-3057-9784"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Nikola Mirkov","raw_affiliation_strings":["\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"],"raw_orcid":"https://orcid.org/0000-0002-3057-9784","affiliations":[{"raw_affiliation_string":"\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia","institution_ids":["https://openalex.org/I4068193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088960620","display_name":"Nicola Fabiano","orcid":"https://orcid.org/0000-0003-1645-2071"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Nicola Fabiano","raw_affiliation_strings":["\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"],"raw_orcid":"https://orcid.org/0000-0003-1645-2071","affiliations":[{"raw_affiliation_string":"\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia","institution_ids":["https://openalex.org/I4068193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086708845","display_name":"Du\u0161an Nikezi\u0107","orcid":"https://orcid.org/0000-0002-8885-2683"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Du\u0161an Nikezi\u0107","raw_affiliation_strings":["\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"],"raw_orcid":"https://orcid.org/0000-0002-8885-2683","affiliations":[{"raw_affiliation_string":"\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia","institution_ids":["https://openalex.org/I4068193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046160337","display_name":"Vuk Stojiljkovi\u0107","orcid":"https://orcid.org/0000-0002-4244-4342"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Vuk Stojiljkovi\u0107","raw_affiliation_strings":["Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia"],"raw_orcid":"https://orcid.org/0000-0002-4244-4342","affiliations":[{"raw_affiliation_string":"Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055253987","display_name":"Milica Ili\u0107","orcid":"https://orcid.org/0000-0003-4546-782X"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Milica Ili\u0107","raw_affiliation_strings":["\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"],"raw_orcid":"https://orcid.org/0000-0003-4546-782X","affiliations":[{"raw_affiliation_string":"\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia","institution_ids":["https://openalex.org/I4068193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056432133"],"corresponding_institution_ids":["https://openalex.org/I4068193"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.8263,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86238136,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"17","issue":"1","first_page":"47","last_page":"47"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6883062124252319},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.6455895900726318},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5365979671478271},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5286203622817993},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5253412127494812},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4547712802886963},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.45351850986480713},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4409506916999817},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.43633705377578735},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4274919629096985},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.415516197681427},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3379749059677124},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.2689530849456787},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.22566398978233337},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15561407804489136},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0868520736694336},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.08578792214393616}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6883062124252319},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.6455895900726318},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5365979671478271},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5286203622817993},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5253412127494812},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4547712802886963},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.45351850986480713},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4409506916999817},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.43633705377578735},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4274919629096985},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.415516197681427},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3379749059677124},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.2689530849456787},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.22566398978233337},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15561407804489136},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0868520736694336},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.08578792214393616},{"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym17010047","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010047","pdf_url":"https://www.mdpi.com/2073-8994/17/1/47/pdf?version=1735558015","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:b8142b4141fd42a48853dbf7b6767f3c","is_oa":false,"landing_page_url":"https://doaj.org/article/b8142b4141fd42a48853dbf7b6767f3c","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 47 (2024)","raw_type":"article"},{"id":"pmh:oai:vinar.vin.bg.ac.rs:123456789/14235","is_oa":true,"landing_page_url":"https://vinar.vin.bg.ac.rs/handle/123456789/14235","pdf_url":null,"source":{"id":"https://openalex.org/S4306402108","display_name":"VinaR (Institute of Nuclear Sciences \"Vin\u010da\")","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210101313","host_organization_name":"University Hospital Center Dr Dragi\u0161a Mi\u0161ovi\u0107","host_organization_lineage":["https://openalex.org/I4210101313"],"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":"article"}],"best_oa_location":{"id":"doi:10.3390/sym17010047","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010047","pdf_url":"https://www.mdpi.com/2073-8994/17/1/47/pdf?version=1735558015","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405928056.pdf","grobid_xml":"https://content.openalex.org/works/W4405928056.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1151736479","https://openalex.org/W1490180844","https://openalex.org/W1506472753","https://openalex.org/W1627568958","https://openalex.org/W1635622277","https://openalex.org/W1964806652","https://openalex.org/W1977373378","https://openalex.org/W1981115560","https://openalex.org/W1992210339","https://openalex.org/W2000823304","https://openalex.org/W2001816900","https://openalex.org/W2043574450","https://openalex.org/W2045039179","https://openalex.org/W2051478763","https://openalex.org/W2053688437","https://openalex.org/W2068061505","https://openalex.org/W2072540444","https://openalex.org/W2078290517","https://openalex.org/W2086213908","https://openalex.org/W2529342090","https://openalex.org/W2799298765","https://openalex.org/W3021821037","https://openalex.org/W3022791782","https://openalex.org/W3119641555","https://openalex.org/W4247375400","https://openalex.org/W4393408487","https://openalex.org/W4396663530","https://openalex.org/W6644650131","https://openalex.org/W6664231378"],"related_works":["https://openalex.org/W4255016916","https://openalex.org/W2095163884","https://openalex.org/W2150070385","https://openalex.org/W2791210196","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W2000247808","https://openalex.org/W2060099884","https://openalex.org/W1987365920","https://openalex.org/W2952825496"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3],"discuss":[4],"the":[5,17,39,74,87,123,127,130,140,145],"symmetries":[6,31],"underlying":[7],"Bernstein":[8,111],"polynomial":[9,44,94,131],"differentiation":[10,45,59,141],"matrices,":[11,142],"as":[12,175],"they":[13],"are":[14,32,63],"used":[15],"in":[16,65,139],"collocation":[18,149],"method":[19,42,83],"approach":[20,166],"to":[21,101,153],"approximate":[22],"solutions":[23,67],"of":[24,38,58,68,78,89,110,117,129,148],"initial":[25,70],"and":[26,54,98,122,156,163],"boundary":[27],"value":[28,71],"problems.":[29],"The":[30,47,61,82,108],"brought":[33],"into":[34],"connection":[35],"with":[36,144],"those":[37],"Chebyshev":[40,176],"pseudospectral":[41,167],"(Chebyshev":[43],"matrices).":[46],"treatment":[48],"discussed":[49],"here":[50],"enables":[51],"a":[52,103,114],"faster":[53],"more":[55],"accurate":[56,155],"generation":[57],"matrices.":[60],"results":[62],"applied":[64],"numerical":[66,91,158],"several":[69],"problems":[72],"for":[73,119,160],"partial":[75],"differential":[76],"equation":[77],"convection\u2013diffusion":[79],"reaction":[80],"type.":[81],"described":[84],"herein":[85],"demonstrates":[86],"combination":[88],"advanced":[90],"techniques":[92],"like":[93],"interpolation,":[95],"stability-preserving":[96],"timestepping,":[97],"transformation":[99],"methods":[100,159,168],"solve":[102],"challenging":[104],"nonlinear":[105],"PDE":[106],"efficiently.":[107],"use":[109,170],"polynomials":[112,173],"offers":[113],"high":[115],"degree":[116],"accuracy":[118,164],"spatial":[120],"discretization,":[121],"CGL":[124],"nodes":[125,150],"improve":[126],"stability":[128],"approximation.":[132],"This":[133],"analysis":[134],"shows":[135],"that":[136,165,169],"exploiting":[137],"symmetry":[138],"combined":[143],"wise":[146],"choice":[147],"(CGL),":[151],"leads":[152],"both":[154],"efficient":[157],"solving":[161],"PDEs":[162],"well-known":[171],"orthogonal":[172],"such":[174],"polynomials.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}