{"id":"https://openalex.org/W3021899781","doi":"https://doi.org/10.1155/2020/5163704","title":"A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations","display_name":"A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations","publication_year":2020,"publication_date":"2020-04-30","ids":{"openalex":"https://openalex.org/W3021899781","doi":"https://doi.org/10.1155/2020/5163704","mag":"3021899781"},"language":"en","primary_location":{"id":"doi:10.1155/2020/5163704","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/5163704","pdf_url":"http://downloads.hindawi.com/journals/complexity/2020/5163704.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/complexity/2020/5163704.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007378403","display_name":"Philku Lee","orcid":"https://orcid.org/0000-0002-1205-6664"},"institutions":[{"id":"https://openalex.org/I99041443","display_name":"Mississippi State University","ror":"https://ror.org/0432jq872","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I99041443"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Philku Lee","raw_affiliation_strings":["Department of Mathematics and Statistics, Mississippi State University, Starkville, Mississippi State, MS 39762, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Mississippi State University, Starkville, Mississippi State, MS 39762, USA","institution_ids":["https://openalex.org/I99041443"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047082789","display_name":"George V. Popescu","orcid":"https://orcid.org/0000-0002-7580-6792"},"institutions":[{"id":"https://openalex.org/I4210098735","display_name":"National Institute for Laser Plasma and Radiation Physics","ror":"https://ror.org/01468by48","country_code":"RO","type":"facility","lineage":["https://openalex.org/I4210098735"]},{"id":"https://openalex.org/I99041443","display_name":"Mississippi State University","ror":"https://ror.org/0432jq872","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I99041443"]}],"countries":["RO","US"],"is_corresponding":true,"raw_author_name":"George V. Popescu","raw_affiliation_strings":["Institute for Genomics, Biocomputing and Biotechnology, Mississippi State University, Starkville, Mississippi State, MS 39762, USA","The National Institute for Laser, Plasma & Radiation Physics, 077126 M\u0103gurele, Ilfov, Romania"],"affiliations":[{"raw_affiliation_string":"Institute for Genomics, Biocomputing and Biotechnology, Mississippi State University, Starkville, Mississippi State, MS 39762, USA","institution_ids":["https://openalex.org/I99041443"]},{"raw_affiliation_string":"The National Institute for Laser, Plasma & Radiation Physics, 077126 M\u0103gurele, Ilfov, Romania","institution_ids":["https://openalex.org/I4210098735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052797183","display_name":"Seongjai Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I99041443","display_name":"Mississippi State University","ror":"https://ror.org/0432jq872","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I99041443"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Seongjai Kim","raw_affiliation_strings":["Department of Mathematics and Statistics, Mississippi State University, Starkville, Mississippi State, MS 39762, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Mississippi State University, Starkville, Mississippi State, MS 39762, USA","institution_ids":["https://openalex.org/I99041443"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047082789"],"corresponding_institution_ids":["https://openalex.org/I4210098735","https://openalex.org/I99041443"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.1821,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76036119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9987000226974487,"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":0.9987000226974487,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9955000281333923,"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/spurious-relationship","display_name":"Spurious relationship","score":0.8616542220115662},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.7069439888000488},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.5867416262626648},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5780106782913208},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5560909509658813},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5080556869506836},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48948490619659424},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4702044129371643},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46011263132095337},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.439716100692749},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.42436283826828003},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3538600504398346},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11317625641822815},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0759522020816803}],"concepts":[{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.8616542220115662},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.7069439888000488},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.5867416262626648},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5780106782913208},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5560909509658813},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5080556869506836},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48948490619659424},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4702044129371643},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46011263132095337},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.439716100692749},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.42436283826828003},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3538600504398346},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11317625641822815},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0759522020816803},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.0},{"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:10.1155/2020/5163704","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/5163704","pdf_url":"http://downloads.hindawi.com/journals/complexity/2020/5163704.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:5163704","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/5163704.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:4ad2f4795fed4775a09cf3f64f1e1a39","is_oa":true,"landing_page_url":"https://doaj.org/article/4ad2f4795fed4775a09cf3f64f1e1a39","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/5163704","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/5163704","pdf_url":"http://downloads.hindawi.com/journals/complexity/2020/5163704.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4263571063","display_name":"Collaborative Research: Function and Regulation of Thimet Oligopeptidase-Mediated Proteolytic Pathways in Plant Stress","funder_award_id":"1714157","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G84140598","display_name":null,"funder_award_id":"NSF-MCB","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3021899781.pdf","grobid_xml":"https://content.openalex.org/works/W3021899781.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1268400865","https://openalex.org/W1592415565","https://openalex.org/W1625555799","https://openalex.org/W1785951909","https://openalex.org/W1980661496","https://openalex.org/W1998666864","https://openalex.org/W2001538622","https://openalex.org/W2018356291","https://openalex.org/W2024453017","https://openalex.org/W2027244891","https://openalex.org/W2029870529","https://openalex.org/W2031166205","https://openalex.org/W2034809969","https://openalex.org/W2037486322","https://openalex.org/W2053865685","https://openalex.org/W2064272232","https://openalex.org/W2065330829","https://openalex.org/W2068769173","https://openalex.org/W2082395037","https://openalex.org/W2089840306","https://openalex.org/W2095036901","https://openalex.org/W2107148630","https://openalex.org/W2153207859","https://openalex.org/W2167657634","https://openalex.org/W2793939407","https://openalex.org/W2969482691","https://openalex.org/W4240486313","https://openalex.org/W4246241682"],"related_works":["https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2162899405","https://openalex.org/W2044987316","https://openalex.org/W2237480245","https://openalex.org/W3134374554","https://openalex.org/W2091480169","https://openalex.org/W4226416379","https://openalex.org/W2064123187","https://openalex.org/W4367359664"],"abstract_inverted_index":{"After":[0],"a":[1,35,62,71,79,111,129],"theory":[2],"of":[3,22,81,94,110,122,136],"morphogenesis":[4],"in":[5,10,182],"chemical":[6],"cells":[7],"was":[8],"introduced":[9],"the":[11,19,41,52,82,89,100,123,133,144,152,157,161,170,178],"1950s,":[12],"much":[13,148],"attention":[14],"had":[15],"been":[16,34],"devoted":[17],"to":[18,97,119,141,151],"numerical":[20,134,145],"solution":[21,101,135,146],"reaction-diffusion":[23],"(RD)":[24],"partial":[25],"differential":[26],"equations":[27],"(PDEs).":[28],"The":[29,103,125],"Crank\u2013Nicolson":[30],"(CN)":[31],"method":[32,43,76,91,172,180],"has":[33],"common":[36],"second-order":[37,64,112],"time-stepping":[38,65,105],"procedure.":[39],"However,":[40],"CN":[42,83,171],"may":[44,173],"introduce":[45],"spurious":[46,175],"oscillations":[47,96],"for":[48,67,132,166],"nonsmooth":[49],"data":[50],"unless":[51],"time":[53,87],"step":[54],"size":[55],"is":[56,107,147],"sufficiently":[57],"small.":[58],"This":[59],"article":[60,126],"studies":[61],"nonoscillatory":[63,108],"procedure":[66,106],"RD":[68],"equations,":[69],"called":[70],"variable-":[72],"<mml:math":[73],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[74],"id=\"M1\"><mml:mi>\u03b8</mml:mi></mml:math>":[75],",":[77],"as":[78],"perturbation":[80],"method.":[84,124],"In":[85],"each":[86],"level,":[88],"new":[90],"detects":[92],"points":[93],"potential":[95],"implicitly":[98],"resolve":[99],"there.":[102],"proposed":[104,179],"and":[109],"temporal":[113,158],"accuracy.":[114],"Various":[115],"examples":[116],"are":[117],"given":[118],"show":[120],"effectiveness":[121],"also":[127],"performs":[128],"sensitivity":[130],"analysis":[131],"biological":[137],"pattern":[138],"forming":[139],"models":[140],"conclude":[142],"that":[143],"more":[149],"sensitive":[150],"spatial":[153,162],"mesh":[154],"resolution":[155,163],"than":[156],"one.":[159],"As":[160],"becomes":[164],"higher":[165],"an":[167],"improved":[168],"accuracy,":[169],"produce":[174],"oscillations,":[176],"while":[177],"results":[181],"stable":[183],"solutions.":[184]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}