{"id":"https://openalex.org/W2011821155","doi":"https://doi.org/10.1080/00207160701864475","title":"An efficient implementation of a numerical method for a chemotaxis system","display_name":"An efficient implementation of a numerical method for a chemotaxis system","publication_year":2008,"publication_date":"2008-12-06","ids":{"openalex":"https://openalex.org/W2011821155","doi":"https://doi.org/10.1080/00207160701864475","mag":"2011821155"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701864475","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701864475","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5060323110","display_name":"Michael W. Smiley","orcid":null},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael W. Smiley","raw_affiliation_strings":["\n Department of Mathematics, Iowa State University, Ames, IA, USA","Department of Mathematics, Iowa State University, Ames, IA, USA"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics, Iowa State University, Ames, IA, USA","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA, USA","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060323110"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":1.0404,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.76944359,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"86","issue":"2","first_page":"219","last_page":"235"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9950000047683716,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9574000239372253,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/stencil","display_name":"Stencil","score":0.6751395463943481},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.6055400371551514},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5938094258308411},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5929387211799622},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5672779679298401},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.522636890411377},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.46841517090797424},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.46528878808021545},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4219302535057068},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4166700839996338},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37669456005096436},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22987216711044312},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.14408648014068604},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11735966801643372},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07811552286148071}],"concepts":[{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.6751395463943481},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.6055400371551514},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5938094258308411},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5929387211799622},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5672779679298401},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.522636890411377},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.46841517090797424},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.46528878808021545},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4219302535057068},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4166700839996338},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37669456005096436},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22987216711044312},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.14408648014068604},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11735966801643372},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07811552286148071},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701864475","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701864475","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1760551737","https://openalex.org/W1902819800","https://openalex.org/W1990930428","https://openalex.org/W2031441801","https://openalex.org/W2042892258","https://openalex.org/W2134572726","https://openalex.org/W2143476164","https://openalex.org/W4206097460","https://openalex.org/W4301491118"],"related_works":["https://openalex.org/W3105129168","https://openalex.org/W2804920739","https://openalex.org/W4316371992","https://openalex.org/W2186216222","https://openalex.org/W2392765154","https://openalex.org/W2564509292","https://openalex.org/W2008005532","https://openalex.org/W1971603802","https://openalex.org/W1795008753","https://openalex.org/W3011358647"],"abstract_inverted_index":{"Abstract":[0],"A":[1,36],"system":[2,25],"of":[3,10,13,32,50,58,65,125],"partial":[4],"differential":[5],"equations":[6],"modelling":[7],"the":[8,56,66,86,93,101,122],"attraction":[9],"a":[11,16,69],"population":[12],"cells":[14],"to":[15],"biochemical":[17],"concentration":[18],"in":[19,55,68],"its":[20],"environment":[21],"is":[22,39,72,89,99],"considered.":[23],"The":[24],"incorporates":[26],"convective":[27],"and":[28,52],"diffusive":[29],"effects,":[30],"either":[31,80,97],"which":[33,47],"may":[34],"dominate.":[35],"numerical":[37],"method":[38,67],"presented":[40],"that":[41,74,92],"allows":[42],"for":[43,79,96],"both":[44],"possible":[45],"features,":[46],"conserves":[48],"positivity":[49],"solutions":[51],"their":[53],"mass":[54],"absence":[57],"sources":[59],"or":[60,82],"sinks.":[61],"An":[62],"efficient":[63],"implementation":[64],"two-dimensional":[70],"setting":[71],"described":[73],"uses":[75],"fast":[76],"Poisson":[77,106],"solvers":[78],"5-":[81],"9-pt":[83],"stencils":[84],"approximating":[85],"Laplacian.":[87],"It":[88],"also":[90],"shown":[91],"computational":[94],"work":[95,116],"stencil":[98],"essentially":[100],"same.":[102],"Keywords:":[103],"chemotaxisconvectiondiffusion9-pt":[104],"stencilfast":[105],"solver":[107],"2000":[108],"AMS":[109],"Subject":[110],"Classification":[111],":":[112],"65M0665M1265M25":[113],"Acknowledgements":[114],"This":[115],"has":[117],"been":[118],"partially":[119],"supported":[120],"by":[121],"National":[123],"Institutes":[124],"Health":[126],"under":[127],"contract":[128],"grant":[129],"number":[130],"R01":[131],"GM072005-01.":[132]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}