{"id":"https://openalex.org/W2002442505","doi":"https://doi.org/10.1137/050643210","title":"A Predictor\u2010Corrector Algorithm for Reaction\u2010Diffusion Equations Associated with Neural Activity on Branched Structures","display_name":"A Predictor\u2010Corrector Algorithm for Reaction\u2010Diffusion Equations Associated with Neural Activity on Branched Structures","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2002442505","doi":"https://doi.org/10.1137/050643210","mag":"2002442505"},"language":"en","primary_location":{"id":"doi:10.1137/050643210","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050643210","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/A5067318148","display_name":"Michael J. Rempe","orcid":"https://orcid.org/0000-0001-7552-9548"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. J. Rempe","raw_affiliation_strings":["Northwestern University****"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northwestern University****","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027192132","display_name":"David L. Chopp","orcid":"https://orcid.org/0000-0003-4270-6426"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. L. Chopp","raw_affiliation_strings":["Engineering Sciences and Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering Sciences and Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2796,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.54496477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"6","first_page":"2139","last_page":"2161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5898663401603699},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5776510238647461},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5654695630073547},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5425072908401489},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.4768725037574768},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.472512811422348},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4474143087863922},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44418686628341675},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4270382821559906},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42159321904182434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38283658027648926},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.362795889377594},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21775811910629272},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17521008849143982},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09771695733070374}],"concepts":[{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5898663401603699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5776510238647461},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5654695630073547},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5425072908401489},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.4768725037574768},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.472512811422348},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4474143087863922},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44418686628341675},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4270382821559906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42159321904182434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38283658027648926},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.362795889377594},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21775811910629272},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17521008849143982},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09771695733070374},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050643210","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050643210","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1543916717","https://openalex.org/W1855000541","https://openalex.org/W1985378448","https://openalex.org/W1985940938","https://openalex.org/W1988479803","https://openalex.org/W2039647139","https://openalex.org/W2065799397","https://openalex.org/W2071007053","https://openalex.org/W2076148352","https://openalex.org/W2117120818","https://openalex.org/W2149878863","https://openalex.org/W2167657634","https://openalex.org/W2168779967"],"related_works":["https://openalex.org/W4212973497","https://openalex.org/W1980786482","https://openalex.org/W2360550119","https://openalex.org/W3177208105","https://openalex.org/W3165035967","https://openalex.org/W2389963024","https://openalex.org/W2353849135","https://openalex.org/W3085591969","https://openalex.org/W1943105110","https://openalex.org/W2058628803"],"abstract_inverted_index":{"In":[0,51],"this":[1,75],"paper,":[2],"we":[3],"present":[4],"a":[5,35,47,82,91,106,113,150],"numerical":[6],"method":[7,17,76],"for":[8,58,123],"solving":[9],"reaction\u2010diffusion":[10],"equations":[11,30,110],"on":[12,100],"one\u2010dimensional":[13,92],"branched":[14,93],"structures.":[15],"The":[16],"effectively":[18,88],"decouples":[19],"the":[20,24,29,62,78,96,101,127,138],"many":[21],"branches":[22],"at":[23],"nodal":[25],"junctions":[26],"so":[27],"that":[28,40],"can":[31,69,86],"be":[32,70,87],"solved":[33],"as":[34,90,126],"system":[36],"of":[37,49,81,108,129,144],"smaller":[38],"problems":[39],"are":[41,64,105,120],"purely":[42],"tridiagonal.":[43],"This":[44],"strategy":[45],"enables":[46],"number":[48],"improvements.":[50],"particular,":[52],"difficulties":[53],"associated":[54],"with":[55,141],"implicit":[56],"methods":[57,119],"closed":[59],"loops":[60],"in":[61,135,153],"network":[63,145],"eliminated,":[65],"and":[66,95],"spatial":[67],"adaptivity":[68],"easily":[71],"implemented.":[72],"We":[73],"apply":[74],"to":[77,112],"electrical":[79],"activity":[80,130,142],"neuron.":[83],"A":[84],"neuron":[85],"represented":[89],"structure,":[94],"model":[97],"equations,":[98,104],"based":[99],"Hodgkin\u2013Huxley":[102],"cable":[103],"set":[107],"reaction":[109],"coupled":[111],"single":[114],"diffusion":[115],"process.":[116],"Spatially":[117],"adaptive":[118],"particularly":[121],"effective":[122],"neuronal":[124],"simulations":[125],"region":[128],"is":[131],"often":[132],"very":[133],"localized":[134],"space.":[136],"Since":[137],"algorithm":[139],"scales":[140],"instead":[143],"size,":[146],"it":[147],"will":[148],"make":[149],"substantial":[151],"reduction":[152],"computational":[154],"cost":[155],"over":[156],"existing":[157],"methods.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
