{"id":"https://openalex.org/W2058421692","doi":"https://doi.org/10.1090/s0025-5718-09-02317-5","title":"On some fast well-balanced first order solvers for nonconservative systems","display_name":"On some fast well-balanced first order solvers for nonconservative systems","publication_year":2009,"publication_date":"2009-11-23","ids":{"openalex":"https://openalex.org/W2058421692","doi":"https://doi.org/10.1090/s0025-5718-09-02317-5","mag":"2058421692"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-09-02317-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02317-5","pdf_url":"https://www.ams.org/mcom/2010-79-271/S0025-5718-09-02317-5/S0025-5718-09-02317-5.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/2010-79-271/S0025-5718-09-02317-5/S0025-5718-09-02317-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005054247","display_name":"Manuel J. Castro","orcid":"https://orcid.org/0000-0003-3164-7715"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manuel Castro","raw_affiliation_strings":["Universidad de M\u00c3\u00a1laga, Departamento An\u00c3\u00a1lisis Matem\u00c3\u00a1tico, Campus de Teatinos s/n, 29071 M\u00c3\u00a1laga, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de M\u00c3\u00a1laga, Departamento An\u00c3\u00a1lisis Matem\u00c3\u00a1tico, Campus de Teatinos s/n, 29071 M\u00c3\u00a1laga, Spain","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007307934","display_name":"Alberto Pardo","orcid":"https://orcid.org/0000-0003-4011-4232"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alberto Pardo","raw_affiliation_strings":["Universidad de M\u00c3\u00a1laga, Departamento An\u00c3\u00a1lisis Matem\u00c3\u00a1tico, Campus de Teatinos s/n, 29071 M\u00c3\u00a1laga, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de M\u00c3\u00a1laga, Departamento An\u00c3\u00a1lisis Matem\u00c3\u00a1tico, Campus de Teatinos s/n, 29071 M\u00c3\u00a1laga, Spain","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011941405","display_name":"Carlos Par\u00e9s","orcid":"https://orcid.org/0000-0002-9545-5635"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos Par\u00e9s","raw_affiliation_strings":["Universidad de M\u00c3\u00a1laga, Departamento An\u00c3\u00a1lisis Matem\u00c3\u00a1tico, Campus de Teatinos s/n, 29071 M\u00c3\u00a1laga, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de M\u00c3\u00a1laga, Departamento An\u00c3\u00a1lisis Matem\u00c3\u00a1tico, Campus de Teatinos s/n, 29071 M\u00c3\u00a1laga, Spain","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030446403","display_name":"Eleuterio F. Toro","orcid":"https://orcid.org/0000-0002-9347-7574"},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"E. Toro","raw_affiliation_strings":["University of Trento. Laboratory of Applied Mathematics. Faculty of Engineering, 38050 Mesiano di Povo, Trento, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Trento. Laboratory of Applied Mathematics. Faculty of Engineering, 38050 Mesiano di Povo, Trento, Italy","institution_ids":["https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.2595,"has_fulltext":true,"cited_by_count":92,"citation_normalized_percentile":{"value":0.97244184,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"79","issue":"271","first_page":"1427","last_page":"1472"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998999834060669,"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":0.9980999827384949,"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":0.9979000091552734,"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":[{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.7722011804580688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7394372820854187},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.559182345867157},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.550547182559967},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.47038283944129944},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3232184052467346}],"concepts":[{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7722011804580688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7394372820854187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.559182345867157},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.550547182559967},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47038283944129944},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3232184052467346},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-09-02317-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02317-5","pdf_url":"https://www.ams.org/mcom/2010-79-271/S0025-5718-09-02317-5/S0025-5718-09-02317-5.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:10.1.1.160.2693","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.2693","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/mcom/0000-000-00/S0025-5718-09-02317-5/S0025-5718-09-02317-5.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.188.9376","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.188.9376","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/2010-79-271/S0025-5718-09-02317-5/S0025-5718-09-02317-5.pdf","raw_type":"text"},{"id":"pmh:oai:iris.unitn.it:11572/332145","is_oa":false,"landing_page_url":"http://hdl.handle.net/11572/332145","pdf_url":null,"source":{"id":"https://openalex.org/S4306401913","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unitn.it:11572/51214","is_oa":false,"landing_page_url":"http://hdl.handle.net/11572/51214","pdf_url":null,"source":{"id":"https://openalex.org/S4377196320","display_name":"Iris (University of Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-09-02317-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02317-5","pdf_url":"https://www.ams.org/mcom/2010-79-271/S0025-5718-09-02317-5/S0025-5718-09-02317-5.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":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.46000000834465027}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311265","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2058421692.pdf","grobid_xml":"https://content.openalex.org/works/W2058421692.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W115528814","https://openalex.org/W348217116","https://openalex.org/W1489409145","https://openalex.org/W1971166309","https://openalex.org/W1975096556","https://openalex.org/W1975628738","https://openalex.org/W1981001745","https://openalex.org/W1985715533","https://openalex.org/W1998602489","https://openalex.org/W2020752851","https://openalex.org/W2029839504","https://openalex.org/W2031043673","https://openalex.org/W2031801811","https://openalex.org/W2041314330","https://openalex.org/W2046863157","https://openalex.org/W2061726168","https://openalex.org/W2068056613","https://openalex.org/W2077620382","https://openalex.org/W2078213066","https://openalex.org/W2089134771","https://openalex.org/W2110401007","https://openalex.org/W2112150873","https://openalex.org/W2128506141","https://openalex.org/W2136592480","https://openalex.org/W2142492132","https://openalex.org/W2152122438","https://openalex.org/W2155785405","https://openalex.org/W2171431553","https://openalex.org/W2482838170","https://openalex.org/W6662292961","https://openalex.org/W6679017083"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W2165950148","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W4300101996","https://openalex.org/W3101625811","https://openalex.org/W2999135108","https://openalex.org/W2363340714"],"abstract_inverted_index":{"The":[0,39,127],"goal":[1,111],"of":[2,45,52,65,68,103,106,166,178,196],"this":[3,71,125],"article":[4],"is":[5,48,113,129,158],"to":[6,24,78,114,130,141,148,152,160,175,192],"design":[7,115],"robust":[8],"and":[9,86,151,184],"simple":[10],"first":[11],"order":[12,32],"explicit":[13,101],"solvers":[14,21,47],"for":[15,30,34,42],"one-dimensional":[16],"nonconservative":[17,79,176],"hyperbolic":[18],"systems.":[19,80],"These":[20,81],"are":[22,139,190],"intended":[23],"be":[25,76],"used":[26,140,159],"as":[27,170],"the":[28,43,49,63,100,104,107,132,143,146,149,153,179,194,197],"basis":[29],"higher":[31],"methods":[33,74,82,117],"one":[35],"or":[36],"multidimensional":[37],"problems.":[38],"starting":[40],"point":[41],"development":[44],"these":[46],"general":[50],"definition":[51],"a":[53,66,120],"Roe":[54,73,121,133,202],"linearization":[55,122],"introduced":[56,199],"by":[57],"Toumi":[58],"in":[59,95],"1992":[60],"based":[61,118],"on":[62,119],"use":[64],"family":[67],"paths.":[69],"Using":[70],"concept,":[72],"can":[75],"extended":[77],"have":[83,91],"good":[84],"well-balanced":[85],"robustness":[87],"properties,":[88],"but":[89],"they":[90],"also":[92],"some":[93,173],"drawbacks:":[94],"particular,":[96],"their":[97],"implementation":[98],"requires":[99],"knowledge":[102],"eigenstructure":[105],"intermediate":[108],"matrices.":[109],"Our":[110],"here":[112,200],"numerical":[116,188],"which":[123,138,168],"overcome":[124],"drawback.":[126],"idea":[128],"split":[131],"matrices":[134],"into":[135],"two":[136,162],"parts":[137],"calculate":[142],"contributions":[144],"at":[145],"cells":[147],"right":[150],"left,":[154],"respectively.":[155],"This":[156],"strategy":[157],"generate":[161],"different":[163],"one-parameter":[164],"families":[165],"schemes":[167,198],"contain,":[169],"particular":[171],"cases,":[172],"generalizations":[174],"systems":[177],"well-known":[180],"Lax-Friedrichs,":[181],"Lax-Wendroff,":[182],"FORCE,":[183],"GFORCE":[185],"schemes.":[186],"Some":[187],"experiments":[189],"presented":[191],"compare":[193],"behaviors":[195],"with":[201],"methods.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}