{"id":"https://openalex.org/W2035810512","doi":"https://doi.org/10.1137/s0036142900370927","title":"A Collocation Method for the Gurtin--MacCamy Equation with Finite Life-Span","display_name":"A Collocation Method for the Gurtin--MacCamy Equation with Finite Life-Span","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2035810512","doi":"https://doi.org/10.1137/s0036142900370927","mag":"2035810512"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900370927","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900370927","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://oasis.postech.ac.kr/handle/2014.oak/12932","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100743278","display_name":"Miyoung Kim","orcid":"https://orcid.org/0000-0002-8903-5044"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mi-Young Kim","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076320252","display_name":"Yonghoon Kwon","orcid":"https://orcid.org/0000-0002-6232-4305"},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Yonghoon Kwon","raw_affiliation_strings":["Pohang University of Science and Technology"],"affiliations":[{"raw_affiliation_string":"Pohang University of Science and Technology","institution_ids":["https://openalex.org/I123900574"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100743278"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6094,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.88257223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"39","issue":"6","first_page":"1914","last_page":"1937"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9973000288009644,"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":0.9973000288009644,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8808890581130981},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7712413668632507},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.6961437463760376},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.6309560537338257},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.6118819117546082},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6052210927009583},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5212743282318115},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.4988851547241211},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4657277464866638},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4568496644496918},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4496408998966217},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4395561218261719},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42624953389167786},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.302114337682724},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2142218053340912}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8808890581130981},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7712413668632507},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.6961437463760376},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.6309560537338257},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.6118819117546082},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6052210927009583},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5212743282318115},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4988851547241211},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4657277464866638},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4568496644496918},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4496408998966217},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4395561218261719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42624953389167786},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.302114337682724},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2142218053340912},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142900370927","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900370927","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:oasis.postech.ac.kr:2014.oak/12932","is_oa":true,"landing_page_url":"https://oasis.postech.ac.kr/handle/2014.oak/12932","pdf_url":null,"source":{"id":"https://openalex.org/S4306401965","display_name":"Open Access System for Information Sharing (Pohang University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123900574","host_organization_name":"Pohang University of Science and Technology","host_organization_lineage":["https://openalex.org/I123900574"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:oasis.postech.ac.kr:2014.oak/12932","is_oa":true,"landing_page_url":"https://oasis.postech.ac.kr/handle/2014.oak/12932","pdf_url":null,"source":{"id":"https://openalex.org/S4306401965","display_name":"Open Access System for Information Sharing (Pohang University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123900574","host_organization_name":"Pohang University of Science and Technology","host_organization_lineage":["https://openalex.org/I123900574"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Responsible consumption and production","id":"https://metadata.un.org/sdg/12","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1540294802","https://openalex.org/W1969006354","https://openalex.org/W1977750259","https://openalex.org/W1990637093","https://openalex.org/W1994988165","https://openalex.org/W1995426250","https://openalex.org/W1999698136","https://openalex.org/W2021312711","https://openalex.org/W2039172636","https://openalex.org/W2049497092","https://openalex.org/W2060292413","https://openalex.org/W2067138440","https://openalex.org/W2067230029","https://openalex.org/W2079976775","https://openalex.org/W2083321256","https://openalex.org/W2091357411","https://openalex.org/W2142740936","https://openalex.org/W2242120026","https://openalex.org/W3023285833","https://openalex.org/W4230374657","https://openalex.org/W4250957121","https://openalex.org/W4285230367"],"related_works":["https://openalex.org/W1482343169","https://openalex.org/W4206513033","https://openalex.org/W3026179575","https://openalex.org/W2296924041","https://openalex.org/W1843663759","https://openalex.org/W2384941625","https://openalex.org/W2318462232","https://openalex.org/W3033023825","https://openalex.org/W2132514189","https://openalex.org/W4317876274"],"abstract_inverted_index":{"A":[0],"collocation":[1,39],"method":[2,25,61],"along":[3,35],"the":[4,30,33,36,44,52,60,68,78],"characteristics":[5],"for":[6],"a":[7,20,73],"stiff":[8],"problem":[9],"arising":[10],"from":[11],"population":[12],"dynamics":[13],"is":[14,19,55,62,65,70],"proposed":[15],"and":[16],"analyzed.":[17],"It":[18,64],"fourth":[21,74],"order":[22,75],"implicit":[23],"Runge--Kutta":[24],"of":[26,32,43,51,59],"two":[27],"stage":[28],"to":[29],"integration":[31],"ODE":[34],"characteristics,":[37],"whose":[38],"points":[40],"are":[41,84],"zeros":[42],"linearly":[45],"transformed":[46],"Legendre":[47],"monic":[48],"polynomial.":[49],"Nonnegativity":[50],"numerical":[53,82],"solutions":[54],"shown.":[56],"The":[57],"stability":[58],"discussed.":[63],"proven":[66],"that":[67],"scheme":[69],"convergent":[71],"at":[72],"rate":[76],"in":[77],"maximum":[79],"norm.":[80],"Several":[81],"examples":[83],"presented.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
