{"id":"https://openalex.org/W2081225921","doi":"https://doi.org/10.1007/s002110200406","title":"Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model","display_name":"Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W2081225921","doi":"https://doi.org/10.1007/s002110200406","mag":"2081225921"},"language":"en","primary_location":{"id":"doi:10.1007/s002110200406","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002110200406","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5080402234","display_name":"Gonzalo Galiano","orcid":"https://orcid.org/0000-0001-7381-7060"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gonzalo Galiano","raw_affiliation_strings":["Departamento de Matematicas, Universidad de Oviedo, Avenida de Calvo Sotelo s/n, 33007 Oviedo, Spain (e-mail: {galiano,maria}@orion.ciencias.uniovi.es)\n, , , , , , ES","Departamento de Matematicas, Universidad de Oviedo, Avenida de Calvo Sotelo s/n, 33007 Oviedo, Spain (e-mail: {galiano,maria}@orion.ciencias.uniovi.es) , ES"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matematicas, Universidad de Oviedo, Avenida de Calvo Sotelo s/n, 33007 Oviedo, Spain (e-mail: {galiano,maria}@orion.ciencias.uniovi.es)\n, , , , , , ES","institution_ids":["https://openalex.org/I165339363"]},{"raw_affiliation_string":"Departamento de Matematicas, Universidad de Oviedo, Avenida de Calvo Sotelo s/n, 33007 Oviedo, Spain (e-mail: {galiano,maria}@orion.ciencias.uniovi.es) , ES","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5098415471","display_name":"Mar\ufffda L. Garz\ufffdn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mar\ufffda L. Garz\ufffdn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111883910","display_name":"Ansgar J\ufffdngel","orcid":null},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ansgar J\ufffdngel","raw_affiliation_strings":["Fachbereich Mathematik und Statistik, Universit\u00e4t Konstanz, Fach D193, 78457 Konstanz, Germany, e-mail: juengel@fmi.uni-konstanz.de, DE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Statistik, Universit\u00e4t Konstanz, Fach D193, 78457 Konstanz, Germany, e-mail: juengel@fmi.uni-konstanz.de, DE","institution_ids":["https://openalex.org/I189712700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.7549,"has_fulltext":false,"cited_by_count":99,"citation_normalized_percentile":{"value":0.8538444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"93","issue":"4","first_page":"655","last_page":"673"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9998999834060669,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9980999827384949,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8641296625137329},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8314200639724731},{"id":"https://openalex.org/keywords/symmetrization","display_name":"Symmetrization","score":0.6992935538291931},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5738658905029297},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5546315908432007},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.548066258430481},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5011343955993652},{"id":"https://openalex.org/keywords/population-model","display_name":"Population model","score":0.48209336400032043},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4638635516166687},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4577438235282898},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.44819724559783936},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4124215245246887},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38616037368774414},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10133087635040283}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8641296625137329},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8314200639724731},{"id":"https://openalex.org/C64999384","wikidata":"https://www.wikidata.org/wiki/Q3507967","display_name":"Symmetrization","level":2,"score":0.6992935538291931},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5738658905029297},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5546315908432007},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.548066258430481},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5011343955993652},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.48209336400032043},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4638635516166687},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4577438235282898},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.44819724559783936},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4124215245246887},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38616037368774414},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10133087635040283},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s002110200406","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002110200406","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.32.8429","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.8429","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.fmi.uni-konstanz.de/pub/preprints/2000/preprint-135.ps.Z","raw_type":"text"},{"id":"pmh:oai:kops.uni-konstanz.de:123456789/6298","is_oa":false,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-21507","pdf_url":null,"source":{"id":"https://openalex.org/S4306401487","display_name":"KOPS (University of Konstanz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189712700","host_organization_name":"University of Konstanz","host_organization_lineage":["https://openalex.org/I189712700"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W236298470","https://openalex.org/W587619276","https://openalex.org/W1579114903","https://openalex.org/W1606313170","https://openalex.org/W1969385392","https://openalex.org/W1973118029","https://openalex.org/W1976752429","https://openalex.org/W1979599605","https://openalex.org/W1992831515","https://openalex.org/W1999453278","https://openalex.org/W2003018740","https://openalex.org/W2004947070","https://openalex.org/W2014205890","https://openalex.org/W2016357735","https://openalex.org/W2023111075","https://openalex.org/W2026570637","https://openalex.org/W2033518856","https://openalex.org/W2041142520","https://openalex.org/W2046264547","https://openalex.org/W2049886781","https://openalex.org/W2066496593","https://openalex.org/W2073078790","https://openalex.org/W2119955287","https://openalex.org/W2135557790","https://openalex.org/W2610542513"],"related_works":["https://openalex.org/W2074849352","https://openalex.org/W2029780455","https://openalex.org/W2964072642","https://openalex.org/W4300193992","https://openalex.org/W148042662","https://openalex.org/W2336702490","https://openalex.org/W2964013457","https://openalex.org/W2490141226","https://openalex.org/W2011648757","https://openalex.org/W2803286947"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
