{"id":"https://openalex.org/W20127990","doi":null,"title":"On complex-stepped Runge-Kutta methods for exact time integration of linear PDEs","display_name":"On complex-stepped Runge-Kutta methods for exact time integration of linear PDEs","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W20127990","mag":"20127990"},"language":"en","primary_location":{"id":"mag:20127990","doi":null,"is_oa":false,"landing_page_url":"http://www.magniel.com/jse/C/vol0401C/p128.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5008679957","display_name":"Denis M. Filatov","orcid":"https://orcid.org/0000-0003-0638-1716","observed_orcids":["https://orcid.org/0000-0003-0638-1716"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Denis M. Filatov","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0638-1716","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5008679957"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3904,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55063096,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.9994999766349792,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.9994999766349792,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7718592882156372},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5636591911315918},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5295052528381348},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.4978172779083252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42920345067977905},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.41136810183525085},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40283024311065674},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3756939470767975},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34361767768859863},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.32227784395217896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24391862750053406},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:20127990","doi":null,"is_oa":false,"landing_page_url":"http://www.magniel.com/jse/C/vol0401C/p128.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W3382305","https://openalex.org/W21678818","https://openalex.org/W180980594","https://openalex.org/W184678741","https://openalex.org/W194974748","https://openalex.org/W599070707","https://openalex.org/W604181985","https://openalex.org/W1482517735","https://openalex.org/W1486154979","https://openalex.org/W1518961746","https://openalex.org/W1527296550","https://openalex.org/W1553738528","https://openalex.org/W1570293554","https://openalex.org/W1582715874","https://openalex.org/W1587330868","https://openalex.org/W1980258772","https://openalex.org/W1992770229","https://openalex.org/W2014310255","https://openalex.org/W2022806376","https://openalex.org/W2031555400","https://openalex.org/W2064374691","https://openalex.org/W2080750693","https://openalex.org/W2111623322","https://openalex.org/W2118877769","https://openalex.org/W2119310316","https://openalex.org/W2128930787","https://openalex.org/W2139794367","https://openalex.org/W2493359456","https://openalex.org/W2751023760","https://openalex.org/W2793869493","https://openalex.org/W3113221786","https://openalex.org/W3141750382"],"related_works":["https://openalex.org/W3207019810","https://openalex.org/W3205482575","https://openalex.org/W1989044728","https://openalex.org/W7099374656","https://openalex.org/W2082139169","https://openalex.org/W2101634908","https://openalex.org/W1529363906","https://openalex.org/W7123652555","https://openalex.org/W4309571313","https://openalex.org/W4317810329"],"abstract_inverted_index":{"We":[0],"extend":[1],"the":[2,6,44,52,58,66,70],"approaches":[3],"developed":[4],"in":[5],"papers":[7],"by":[8,17],"Kaps":[9],"and":[10,16,24],"Rentrop":[11],"[Numerische":[12],"Mathematik":[13],"33,":[14],"(1979)]":[15],"Schatzman":[18],"[J.":[19],"Sci.":[20],"Comput.":[21],"17,":[22],"(2002)],":[23],"suggest":[25],"a":[26],"method":[27,71],"for":[28,47,60],"highly":[29],"accurate":[30,55],"time":[31],"integration":[32,56,74],"of":[33,54],"linear":[34],"first-order":[35],"evolutionary":[36],"PDEs.":[37],"The":[38],"main":[39],"idea":[40],"is":[41],"to":[42,57],"generalise":[43],"Runge-Kutta":[45],"methods":[46],"complex":[48,67],"timesteps,":[49],"which":[50],"reduces":[51],"problem":[53],"search":[59],"an":[61],"optimal":[62],"temporal":[63],"path":[64],"on":[65],"plane.":[68],"Theoretically":[69],"admits":[72],"exact":[73],"with":[75],"finite":[76],"timesteps.":[77]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}