{"id":"https://openalex.org/W2061353257","doi":"https://doi.org/10.1137/050627885","title":"An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular Polygons","display_name":"An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular Polygons","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2061353257","doi":"https://doi.org/10.1137/050627885","mag":"2061353257"},"language":"en","primary_location":{"id":"doi:10.1137/050627885","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050627885","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066709922","display_name":"Bernard Bialecki","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bernard Bialecki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056234867","display_name":"Ryan I. Fernandes","orcid":"https://orcid.org/0000-0002-5176-8250"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ryan I. Fernandes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1316,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90870113,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"3","first_page":"1054","last_page":"1077"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"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"}},"topics":[{"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13685","display_name":"Material Science and Thermodynamics","score":0.9682999849319458,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8625764846801758},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6836049556732178},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.6291951537132263},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5954408645629883},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5355413556098938},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5245901942253113},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.483467161655426},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.4735514223575592},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.43380624055862427},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.4172383248806},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.33073610067367554},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32681208848953247},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.2887551188468933},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12554925680160522}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8625764846801758},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6836049556732178},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.6291951537132263},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5954408645629883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5355413556098938},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5245901942253113},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.483467161655426},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.4735514223575592},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.43380624055862427},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.4172383248806},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33073610067367554},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32681208848953247},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.2887551188468933},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12554925680160522},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer 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/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050627885","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050627885","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W577962163","https://openalex.org/W597907832","https://openalex.org/W1902819800","https://openalex.org/W1969810270","https://openalex.org/W1970643355","https://openalex.org/W2010165577","https://openalex.org/W2031753742","https://openalex.org/W2033071189","https://openalex.org/W2033800650","https://openalex.org/W2035555838","https://openalex.org/W2036044118","https://openalex.org/W2037838607","https://openalex.org/W2039986166","https://openalex.org/W2040474540","https://openalex.org/W2065775687","https://openalex.org/W2076763708","https://openalex.org/W2077636190","https://openalex.org/W2085886206","https://openalex.org/W2095036901","https://openalex.org/W2101930273","https://openalex.org/W2169818181","https://openalex.org/W2987171304","https://openalex.org/W4232082450","https://openalex.org/W4242273588"],"related_works":["https://openalex.org/W4255016916","https://openalex.org/W2095163884","https://openalex.org/W2791210196","https://openalex.org/W2111003632","https://openalex.org/W2380529683","https://openalex.org/W2889856026","https://openalex.org/W2000247808","https://openalex.org/W2952825496","https://openalex.org/W1987365920","https://openalex.org/W2060099884"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,9],"nonlinear":[3],"parabolic":[4],"initial-boundary":[5],"value":[6,31],"problem":[7],"on":[8,102],"rectangular":[10,105,121],"polygon":[11],"with":[12,19,46],"the":[13,25,28,62,65,72,80,85,90,98,103],"solution":[14,26,67,74,92,100],"satisfying":[15],"Robin":[16],"boundary":[17],"conditions":[18],"variable":[20],"coefficients.":[21],"An":[22],"approximation":[23],"to":[24,113,120],"at":[27,84],"desired":[29],"time":[30,60,87],"is":[32,53,89],"obtained":[33],"using":[34],"an":[35,50],"alternating-direction":[36],"implicit":[37],"extrapolated":[38],"Crank--Nicolson":[39],"scheme":[40,63],"in":[41],"which":[42],"orthogonal":[43],"spline":[44],"collocation":[45],"piecewise":[47],"polynomials":[48],"of":[49,109],"arbitrary":[51],"degree":[52],"used":[54],"for":[55],"spatial":[56],"discretization.":[57],"At":[58],"each":[59],"level,":[61],"determines":[64],"intermediate":[66],"along":[68,75,93],"horizontal":[69],"lines":[70,77,95],"and":[71,117],"approximate":[73,91,99],"vertical":[76,94],"passing":[78],"through":[79],"Gauss":[81],"points.":[82],"Only":[83],"last":[86],"level":[88],"converted":[96],"into":[97],"defined":[101],"entire":[104],"polygon.":[106],"This":[107],"property":[108],"our":[110],"approach":[111],"leads":[112],"its":[114,118],"efficient":[115],"implementation":[116],"applicability":[119],"polygons.":[122]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}