{"id":"https://openalex.org/W2053526635","doi":"https://doi.org/10.1137/130911019","title":"Error Estimates for Discrete-Time Approximations of Nonlinear Cross-Diffusion Systems","display_name":"Error Estimates for Discrete-Time Approximations of Nonlinear Cross-Diffusion Systems","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2053526635","doi":"https://doi.org/10.1137/130911019","mag":"2053526635"},"language":"en","primary_location":{"id":"doi:10.1137/130911019","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911019","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011866404","display_name":"Hideki Murakawa","orcid":"https://orcid.org/0000-0002-0309-4394"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hideki Murakawa","raw_affiliation_strings":["FACULTY OF MATHEMATICS, KYUSHU UNIVERSITY"],"affiliations":[{"raw_affiliation_string":"FACULTY OF MATHEMATICS, KYUSHU UNIVERSITY","institution_ids":["https://openalex.org/I135598925"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011866404"],"corresponding_institution_ids":["https://openalex.org/I135598925"],"apc_list":null,"apc_paid":null,"fwci":1.4475,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80262874,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"52","issue":"2","first_page":"955","last_page":"974"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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":0.9997000098228455,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.998199999332428,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9979000091552734,"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/nonlinear-system","display_name":"Nonlinear system","score":0.7797130942344666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7709543704986572},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6302716732025146},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.6269397735595703},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6211690902709961},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6172319054603577},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6024931073188782},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6016079187393188},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28863465785980225}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7797130942344666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7709543704986572},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6302716732025146},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.6269397735595703},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6211690902709961},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6172319054603577},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6024931073188782},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6016079187393188},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28863465785980225},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130911019","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911019","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W104994705","https://openalex.org/W1538929409","https://openalex.org/W1544648253","https://openalex.org/W1970501143","https://openalex.org/W1973118029","https://openalex.org/W1989560273","https://openalex.org/W2005141382","https://openalex.org/W2014205890","https://openalex.org/W2022770433","https://openalex.org/W2035136471","https://openalex.org/W2038581591","https://openalex.org/W2059769570","https://openalex.org/W2080055296","https://openalex.org/W2081225921","https://openalex.org/W2086290393","https://openalex.org/W2089845038","https://openalex.org/W2105582005","https://openalex.org/W2119955287","https://openalex.org/W2157454707","https://openalex.org/W2587143772","https://openalex.org/W2592848977","https://openalex.org/W2922278694"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2969742028"],"abstract_inverted_index":{"This":[0],"paper":[1,48],"is":[2,26,49],"concerned":[3],"with":[4],"nonlinear":[5,14,66],"and":[6,22,67,80],"linear":[7,24,69],"discrete-time":[8,56],"algorithms":[9],"for":[10,63],"cross-diffusion":[11,88],"systems.":[12,89],"The":[13,43],"scheme":[15,29],"corresponds":[16],"to":[17,50],"backward":[18],"differences":[19],"in":[20],"time,":[21],"the":[23,32,55,60,65,68,87],"algorithm":[25],"a":[27],"very-easy-to-implement":[28],"proposed":[30],"by":[31],"author":[33],"[ESAIM":[34],"Math.":[35],"Model.":[36],"Numer.":[37],"Anal.,":[38],"45":[39],"(2011),":[40],"pp.":[41],"1141--1161].":[42],"main":[44],"purpose":[45],"of":[46,54,83,86],"this":[47],"derive":[51],"convergence":[52],"rates":[53],"schemes.":[57],"We":[58,76],"obtain":[59],"same":[61],"orders":[62,73],"both":[64],"scheme.":[70],"Moreover,":[71],"these":[72],"are":[74],"optimal.":[75],"also":[77],"establish":[78],"uniqueness":[79],"regularity":[81],"results":[82],"weak":[84],"solutions":[85]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}