{"id":"https://openalex.org/W1988623758","doi":"https://doi.org/10.1137/s0036142998332852","title":"A Nonstiff Euler Discretization of the Complex Ginzburg--Landau Equation in One Space Dimension","display_name":"A Nonstiff Euler Discretization of the Complex Ginzburg--Landau Equation in One Space Dimension","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1988623758","doi":"https://doi.org/10.1137/s0036142998332852","mag":"1988623758"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998332852","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998332852","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/A5025788465","display_name":"Peter Tak\u00e1\u010d","orcid":"https://orcid.org/0000-0002-8813-1122"},"institutions":[{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Tak\u00e1c","raw_affiliation_strings":["University of Rostock"],"affiliations":[{"raw_affiliation_string":"University of Rostock","institution_ids":["https://openalex.org/I4665924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084423759","display_name":"Ansgar J\u00fcngel","orcid":"https://orcid.org/0000-0003-0633-8929"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ansgar J\u00fcngel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025788465"],"corresponding_institution_ids":["https://openalex.org/I4665924"],"apc_list":null,"apc_paid":null,"fwci":0.4144,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.7181619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"38","issue":"1","first_page":"292","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994999766349792,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9894000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8054795265197754},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7166303396224976},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6633646488189697},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6247251629829407},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.569223940372467},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5218338370323181},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.519885778427124},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5016677379608154},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.47512274980545044},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.47354620695114136},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.45168715715408325},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.4429028630256653},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4109550416469574},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4023217260837555},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3337099552154541},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.305730938911438}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8054795265197754},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7166303396224976},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6633646488189697},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6247251629829407},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.569223940372467},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5218338370323181},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.519885778427124},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5016677379608154},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.47512274980545044},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.47354620695114136},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.45168715715408325},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.4429028630256653},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4109550416469574},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4023217260837555},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3337099552154541},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.305730938911438},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142998332852","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998332852","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1527296550","https://openalex.org/W1594759473","https://openalex.org/W1642891744","https://openalex.org/W1967727259","https://openalex.org/W1977296565","https://openalex.org/W1978941204","https://openalex.org/W1988055686","https://openalex.org/W1990428497","https://openalex.org/W1990515979","https://openalex.org/W1992574622","https://openalex.org/W1999281566","https://openalex.org/W2002542829","https://openalex.org/W2004394647","https://openalex.org/W2004623263","https://openalex.org/W2017611864","https://openalex.org/W2018322710","https://openalex.org/W2023412230","https://openalex.org/W2024204225","https://openalex.org/W2034963843","https://openalex.org/W2037688108","https://openalex.org/W2039876742","https://openalex.org/W2040164287","https://openalex.org/W2046253768","https://openalex.org/W2054391563","https://openalex.org/W2056729811","https://openalex.org/W2065198439","https://openalex.org/W2075857446","https://openalex.org/W2078362444","https://openalex.org/W2081628295","https://openalex.org/W2083490131","https://openalex.org/W2129882201","https://openalex.org/W2141348593","https://openalex.org/W2157599435","https://openalex.org/W2567464022","https://openalex.org/W3022780580","https://openalex.org/W4251840481"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1507702947","https://openalex.org/W2022062253","https://openalex.org/W946352265"],"abstract_inverted_index":{"A":[0],"nonstiff":[1],"discretization":[2],"method":[3],"is":[4,49,105,121],"applied":[5],"to":[6,111],"the":[7,82,87,91,97,103,113,118],"complex":[8],"Ginzburg--Landau":[9],"(CGL)":[10],"equation":[11,48,89,120],"with":[12],"periodic":[13],"boundary":[14],"conditions,":[15],"\\begin{eqnarray*}":[16],"&\\partial_t":[17],"u":[18,22,27],"=":[19,33],"(1+i\\nu)":[20],"\\partial_{xx}^2":[21],"+":[23,31],"Ru":[24],"-":[25],"(1+i\\mu)|u|^2":[26],";":[28],"\\\\":[29],"&u(x":[30],"2\\pi,t)":[32],"u(x,t)":[34],"\\quad\\mbox{":[35],"for":[36,90],"}":[37],"-\\infty":[38],"<":[39,41],"x":[40],"\\infty,\\;":[42],"t\\geq":[43],"0.":[44],"\\end{eqnarray*}":[45],"This":[46],"parabolic":[47],"discretized":[50,119],"first":[51],"in":[52,67,80,102,107],"space":[53],"by":[54,69],"a":[55,61],"truncated":[56,92],"Fourier":[57,63,78,93,100],"series":[58,94],"(that":[59],"is,":[60],"finite":[62],"sum)":[64],"and":[65,86,123],"then":[66],"time":[68],"an":[70,108],"explicit":[71],"Euler":[72],"method.":[73],"The":[74],"exponential":[75],"decay":[76],"of":[77,99,117],"modes":[79,101],"both,":[81],"original":[83],"CGL":[84],"equation,":[85],"resulting":[88],"(independently":[95],"from":[96],"number":[98],"truncation)":[104],"used":[106],"essential":[109],"way":[110],"prove":[112],"nonstiffness.":[114],"Also":[115],"dissipativity":[116],"established":[122],"numerical":[124],"results":[125],"are":[126],"discussed.":[127]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}