{"id":"https://openalex.org/W2059985118","doi":"https://doi.org/10.1137/s0036142998335996","title":"Numerical Solution of Nonlinear Reaction Diffusion Processes","display_name":"Numerical Solution of Nonlinear Reaction Diffusion Processes","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2059985118","doi":"https://doi.org/10.1137/s0036142998335996","mag":"2059985118"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998335996","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998335996","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/A5011631328","display_name":"Marie-No\u00eblle Le Roux","orcid":null},"institutions":[{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Marie-No\u00eblle Le Roux","raw_affiliation_strings":["IMB, Institut de Math\u00e9matiques de Bordeaux, UMR5251, Universit\u00e9 Bordeaux1, 33405 Talence Cedex, FRANCE"],"affiliations":[{"raw_affiliation_string":"IMB, Institut de Math\u00e9matiques de Bordeaux, UMR5251, Universit\u00e9 Bordeaux1, 33405 Talence Cedex, FRANCE","institution_ids":["https://openalex.org/I4210166017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011631328"],"corresponding_institution_ids":["https://openalex.org/I4210166017"],"apc_list":null,"apc_paid":null,"fwci":0.5275,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.70408526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"37","issue":"5","first_page":"1644","last_page":"1656"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991000294685364,"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":0.9991000294685364,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9944000244140625,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8403037786483765},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7528992891311646},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6281218528747559},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6243754029273987},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.6226748824119568},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5897738337516785},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5425042510032654},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5419020056724548},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5310027599334717},{"id":"https://openalex.org/keywords/chemical-equation","display_name":"Chemical equation","score":0.47411563992500305},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.46160024404525757},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4522153437137604},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4400692582130432},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4396359920501709},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4289349913597107},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07842954993247986},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06964889168739319},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05869722366333008}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8403037786483765},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7528992891311646},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6281218528747559},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6243754029273987},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.6226748824119568},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5897738337516785},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5425042510032654},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5419020056724548},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5310027599334717},{"id":"https://openalex.org/C187738980","wikidata":"https://www.wikidata.org/wiki/Q182527","display_name":"Chemical equation","level":2,"score":0.47411563992500305},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.46160024404525757},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4522153437137604},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4400692582130432},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4396359920501709},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4289349913597107},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07842954993247986},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06964889168739319},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05869722366333008},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142998335996","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998335996","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:CiteSeerX.psu:10.1.1.250.5797","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.5797","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0905.2861v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1976938383","https://openalex.org/W1978551359","https://openalex.org/W1983760800","https://openalex.org/W1995385520","https://openalex.org/W1998233671","https://openalex.org/W2000247006","https://openalex.org/W2005766654","https://openalex.org/W2010500031","https://openalex.org/W2036706294","https://openalex.org/W2044565541","https://openalex.org/W2064698982","https://openalex.org/W2067014089","https://openalex.org/W2071389282","https://openalex.org/W2071415470","https://openalex.org/W2073078790","https://openalex.org/W2101288394","https://openalex.org/W2147500254","https://openalex.org/W2318392277","https://openalex.org/W4237857751","https://openalex.org/W4253949081"],"related_works":["https://openalex.org/W2389517732","https://openalex.org/W3099809193","https://openalex.org/W2330951362","https://openalex.org/W346881876","https://openalex.org/W2084108921","https://openalex.org/W281041820","https://openalex.org/W4388240777","https://openalex.org/W2607759403","https://openalex.org/W2106562951","https://openalex.org/W4308910509"],"abstract_inverted_index":{"In":[0],"this":[1,23],"paper,":[2],"the":[3,35,45,55,60,66,69],"author":[4],"considers":[5],"a":[6,12,17,29,50],"nonlinear":[7,13],"reaction":[8],"diffusion":[9],"equation,":[10],"i.e.,":[11],"heat":[14],"equation":[15,24],"with":[16],"source":[18],"term.":[19],"The":[20,63],"solution":[21,57],"of":[22,39,49,68],"may":[25],"blow":[26],"up":[27],"in":[28,37],"finite":[30],"time.":[31],"A":[32],"scheme":[33,70],"for":[34,54,59],"discretization":[36],"time":[38],"that":[40],"problem":[41],"is":[42,52,71],"proposed,":[43],"and":[44,65],"same":[46],"sufficient":[47],"condition":[48],"blowup":[51],"obtained":[53],"numerical":[56],"as":[58],"exact":[61],"solution.":[62],"stability":[64],"convergence":[67],"proved.":[72]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
