{"id":"https://openalex.org/W2019971825","doi":"https://doi.org/10.1090/s0025-5718-01-01362-x","title":"Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems","display_name":"Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems","publication_year":2001,"publication_date":"2001-11-19","ids":{"openalex":"https://openalex.org/W2019971825","doi":"https://doi.org/10.1090/s0025-5718-01-01362-x","mag":"2019971825"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01362-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01362-x","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01362-X/S0025-5718-01-01362-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01362-X/S0025-5718-01-01362-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043561924","display_name":"M. P. Calvo","orcid":"https://orcid.org/0000-0001-5830-9658"},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"M. Calvo","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1tica Aplicada y Computaci\u00c3\u00b3n, Universidad de Valladolid, Valladolid, Spain","Departamento de Matem\u00e1tica Aplicada y Computaci\u00f3n, Universidad de Valladolid, Valladolid, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1tica Aplicada y Computaci\u00c3\u00b3n, Universidad de Valladolid, Valladolid, Spain","institution_ids":["https://openalex.org/I108103353"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada y Computaci\u00f3n, Universidad de Valladolid, Valladolid, Spain#TAB#","institution_ids":["https://openalex.org/I108103353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071774455","display_name":"C. Palencia","orcid":"https://orcid.org/0000-0003-1823-1395"},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"C. Palencia","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1tica Aplicada y Computaci\u00c3\u00b3n, Universidad de Valladolid, Valladolid, Spain","Departamento de Matem\u00e1tica Aplicada y Computaci\u00f3n, Universidad de Valladolid, Valladolid, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1tica Aplicada y Computaci\u00c3\u00b3n, Universidad de Valladolid, Valladolid, Spain","institution_ids":["https://openalex.org/I108103353"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada y Computaci\u00f3n, Universidad de Valladolid, Valladolid, Spain#TAB#","institution_ids":["https://openalex.org/I108103353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043561924"],"corresponding_institution_ids":["https://openalex.org/I108103353"],"apc_list":null,"apc_paid":null,"fwci":3.5543,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.91720835,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"71","issue":"240","first_page":"1529","last_page":"1543"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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 methods for differential equations","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9984999895095825,"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/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.8326736688613892},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8077284097671509},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.7417242527008057},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6931068897247314},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6581441760063171},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5367015600204468},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5173739790916443},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5083114504814148},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5020463466644287},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4709155261516571},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3945740759372711},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3601835072040558},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.35097581148147583},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15892526507377625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1378045678138733}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.8326736688613892},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8077284097671509},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.7417242527008057},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6931068897247314},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6581441760063171},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5367015600204468},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5173739790916443},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5083114504814148},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5020463466644287},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4709155261516571},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3945740759372711},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3601835072040558},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.35097581148147583},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15892526507377625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1378045678138733},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-01-01362-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01362-x","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01362-X/S0025-5718-01-01362-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4814","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4814","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2002-71-240/S0025-5718-01-01362-X/S0025-5718-01-01362-X.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01362-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01362-x","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01362-X/S0025-5718-01-01362-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320328351","display_name":"Junta de Castilla y Le\u00f3n","ror":"https://ror.org/02s8dab97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2019971825.pdf","grobid_xml":"https://content.openalex.org/works/W2019971825.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1509923322","https://openalex.org/W1527296550","https://openalex.org/W1567796010","https://openalex.org/W1600945564","https://openalex.org/W1602120208","https://openalex.org/W1654733076","https://openalex.org/W1955535265","https://openalex.org/W1965251554","https://openalex.org/W1966504425","https://openalex.org/W1971142716","https://openalex.org/W1977981719","https://openalex.org/W1979424590","https://openalex.org/W1979881748","https://openalex.org/W1986988877","https://openalex.org/W1995504856","https://openalex.org/W1999756879","https://openalex.org/W2004623263","https://openalex.org/W2007962250","https://openalex.org/W2009055753","https://openalex.org/W2023868969","https://openalex.org/W2026326366","https://openalex.org/W2031112327","https://openalex.org/W2036208628","https://openalex.org/W2058396451","https://openalex.org/W2060170348","https://openalex.org/W2067870952","https://openalex.org/W2078193948","https://openalex.org/W2082408762","https://openalex.org/W2082621526","https://openalex.org/W2090106683","https://openalex.org/W2091564990","https://openalex.org/W2092429904","https://openalex.org/W2153059802","https://openalex.org/W2165808880","https://openalex.org/W2246044443","https://openalex.org/W2313962207","https://openalex.org/W2480304173","https://openalex.org/W2490615762","https://openalex.org/W2499652971","https://openalex.org/W2587498379","https://openalex.org/W4236206528","https://openalex.org/W4246212225","https://openalex.org/W4248116268","https://openalex.org/W4254092122"],"related_works":["https://openalex.org/W2166601248","https://openalex.org/W2063974582","https://openalex.org/W2347993416","https://openalex.org/W2057106870","https://openalex.org/W2073242482","https://openalex.org/W3120703968","https://openalex.org/W2062216355","https://openalex.org/W1975244310","https://openalex.org/W1220922634","https://openalex.org/W4376508842"],"abstract_inverted_index":{"A":[0,53],"new":[1],"strategy":[2],"to":[3,61,71],"avoid":[4],"the":[5,39,42,72],"order":[6,51,74],"reduction":[7],"of":[8,30,38],"Runge-Kutta":[9],"methods":[10],"when":[11],"integrating":[12],"linear,":[13],"autonomous,":[14],"nonhomogeneous":[15],"initial":[16,46],"boundary":[17],"value":[18,47],"problems":[19],"is":[20,24,56,67],"presented.":[21],"The":[22],"solution":[23],"decomposed":[25],"into":[26],"two":[27],"parts.":[28],"One":[29],"them":[31],"can":[32],"be":[33],"computed":[34],"directly":[35],"in":[36,76],"terms":[37],"data":[40],"and":[41,78],"other":[43],"satisfies":[44],"an":[45],"problem":[48],"without":[49],"any":[50],"reduction.":[52],"numerical":[54],"illustration":[55],"given.":[57],"This":[58],"idea":[59],"applies":[60],"practical":[62],"problems,":[63],"where":[64],"spatial":[65],"discretization":[66],"also":[68],"required,":[69],"leading":[70],"full":[73],"both":[75],"space":[77],"time.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
