{"id":"https://openalex.org/W2076763708","doi":"https://doi.org/10.1137/s1064827501380691","title":"Solving Degenerate Reaction-Diffusion Equations via Variable Step Peaceman--Rachford Splitting","display_name":"Solving Degenerate Reaction-Diffusion Equations via Variable Step Peaceman--Rachford Splitting","publication_year":2003,"publication_date":"2003-12-05","ids":{"openalex":"https://openalex.org/W2076763708","doi":"https://doi.org/10.1137/s1064827501380691","mag":"2076763708"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827501380691","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501380691","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/A5027356395","display_name":"Hanz Martin Cheng","orcid":"https://orcid.org/0000-0002-2481-4995"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"H. Cheng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063304710","display_name":"Ping Lin","orcid":"https://orcid.org/0000-0002-4378-7929"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Lin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080744092","display_name":"Quan Z. Sheng","orcid":"https://orcid.org/0000-0002-3326-4147"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Q. Sheng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109412865","display_name":"Roger C. E. Tan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. C. E. Tan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5027356395"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1318,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.87167215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"4","first_page":"1273","last_page":"1292"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6874142289161682},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5773359537124634},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5508296489715576},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5314095616340637},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5030698180198669},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.49631577730178833},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4852862060070038},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4532613754272461},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44224196672439575},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42153671383857727},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3798702657222748},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08424463868141174}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6874142289161682},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5773359537124634},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5508296489715576},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5314095616340637},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5030698180198669},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.49631577730178833},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4852862060070038},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4532613754272461},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44224196672439575},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42153671383857727},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3798702657222748},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08424463868141174},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1064827501380691","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501380691","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"},{"id":"pmh:oai:discovery.dundee.ac.uk:openaire_cris_publications/842a8d63-9443-483e-b32f-594d8a2b6f5c","is_oa":false,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/842a8d63-9443-483e-b32f-594d8a2b6f5c","pdf_url":null,"source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cheng, H, Lin, P, Sheng, Q & Tan, R C E 2003, 'Solving degenerate reaction-diffusion equations via variable step Peaceman-Rachford splitting', SIAM Journal on Scientific Computing, vol. 25, no. 4, pp. 1273-1292. https://doi.org/10.1137/S1064827501380691","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/104145","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/104145","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W618655928","https://openalex.org/W1597944220","https://openalex.org/W1654733076","https://openalex.org/W1963668706","https://openalex.org/W1975536006","https://openalex.org/W1978486451","https://openalex.org/W1979454325","https://openalex.org/W2013191107","https://openalex.org/W2045131403","https://openalex.org/W2047974047","https://openalex.org/W2050350245","https://openalex.org/W2061287893","https://openalex.org/W2067779435","https://openalex.org/W2069623243","https://openalex.org/W2077221255","https://openalex.org/W2077605706","https://openalex.org/W2080276632","https://openalex.org/W2082534161","https://openalex.org/W2095036901","https://openalex.org/W2099701509","https://openalex.org/W2136173462","https://openalex.org/W2139469908","https://openalex.org/W2152605913","https://openalex.org/W2167796170","https://openalex.org/W2171707956","https://openalex.org/W2407223959","https://openalex.org/W2409090597","https://openalex.org/W2485999475"],"related_works":["https://openalex.org/W2353039109","https://openalex.org/W2077314575","https://openalex.org/W4315588385","https://openalex.org/W4245687327","https://openalex.org/W4315701745","https://openalex.org/W2915367185","https://openalex.org/W1984394483","https://openalex.org/W1964386056","https://openalex.org/W3128039596","https://openalex.org/W3034571081"],"abstract_inverted_index":{"This":[0,28],"paper":[1],"studies":[2],"the":[3,40,53,58,71,84,104,109,115,123,130,134],"numerical":[4,93,124],"solution":[5,125,132],"of":[6,52,57,83,108,133],"two-dimensional":[7,61],"nonlinear":[8],"degenerate":[9],"reaction-diffusion":[10],"differential":[11],"equations":[12,21],"with":[13],"singular":[14],"forcing":[15],"terms":[16],"over":[17,111],"rectangular":[18],"domains.":[19],"The":[20,43,60,77],"considered":[22],"may":[23],"generate":[24],"strong":[25],"quenching":[26,116],"singularities.":[27],"investigation":[29],"focuses":[30],"on":[31,49],"a":[32],"variable":[33,85],"time":[34,44,55],"step":[35,86],"Peaceman--Rachford":[36],"splitting":[37],"method":[38,110],"for":[39,114],"aforementioned":[41],"problem.":[42,117,136],"adaptation":[45],"is":[46,63,74,119],"implemented":[47],"based":[48],"arc-length":[50],"estimations":[51],"first":[54],"derivative":[56],"solution.":[59],"problem":[62],"split":[64],"into":[65],"several":[66],"one-dimensional":[67],"problems":[68],"so":[69],"that":[70,122],"computational":[72],"cost":[73],"significantly":[75],"reduced.":[76],"monotonicity":[78],"and":[79,106],"localized":[80],"linear":[81],"stability":[82],"scheme":[87],"are":[88],"investigated.":[89],"We":[90],"give":[91],"some":[92],"examples":[94],"to":[95,102],"illustrate":[96],"our":[97],"results":[98],"as":[99,101],"well":[100],"demonstrate":[103],"viability":[105],"efficiency":[107],"existing":[112],"methods":[113],"It":[118],"also":[120],"shown":[121],"obtained":[126],"preserves":[127],"important":[128],"propertiesof":[129],"physical":[131],"given":[135]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}