{"id":"https://openalex.org/W2012702868","doi":"https://doi.org/10.1137/110842727","title":"Semi-Implicit Euler Schemes for Ordinary Differential Inclusions","display_name":"Semi-Implicit Euler Schemes for Ordinary Differential Inclusions","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2012702868","doi":"https://doi.org/10.1137/110842727","mag":"2012702868"},"language":"en","primary_location":{"id":"doi:10.1137/110842727","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110842727","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/A5056042309","display_name":"Janosch Rieger","orcid":"https://orcid.org/0000-0002-4372-7264"},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Janosch Rieger","raw_affiliation_strings":["Goethe-Universit\u00e4t Frankfurt am Main (Goethe University Frankfurt)"],"affiliations":[{"raw_affiliation_string":"Goethe-Universit\u00e4t Frankfurt am Main (Goethe University Frankfurt)","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056042309"],"corresponding_institution_ids":["https://openalex.org/I114090438"],"apc_list":null,"apc_paid":null,"fwci":0.6308,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.68135568,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"52","issue":"2","first_page":"895","last_page":"914"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/backward-euler-method","display_name":"Backward Euler method","score":0.8482524156570435},{"id":"https://openalex.org/keywords/explicit-and-implicit-methods","display_name":"Explicit and implicit methods","score":0.8475963473320007},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8143694400787354},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7611222267150879},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.7086979150772095},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.6806734204292297},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.6640943288803101},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.6250398755073547},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5333853363990784},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5241556167602539},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5099571943283081},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4764419198036194},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.4302936792373657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3676380515098572},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3573846220970154},{"id":"https://openalex.org/keywords/exact-differential-equation","display_name":"Exact differential equation","score":0.18886160850524902},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1492084264755249}],"concepts":[{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.8482524156570435},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.8475963473320007},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8143694400787354},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7611222267150879},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.7086979150772095},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.6806734204292297},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6640943288803101},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.6250398755073547},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5333853363990784},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5241556167602539},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5099571943283081},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4764419198036194},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.4302936792373657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3676380515098572},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3573846220970154},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.18886160850524902},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1492084264755249},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110842727","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110842727","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":[{"id":"https://metadata.un.org/sdg/10","score":0.8100000023841858,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W18120132","https://openalex.org/W139711823","https://openalex.org/W1977205883","https://openalex.org/W1979064177","https://openalex.org/W1989932759","https://openalex.org/W1990866326","https://openalex.org/W2019989441","https://openalex.org/W2048389107","https://openalex.org/W2057039419","https://openalex.org/W2057312365","https://openalex.org/W2321182513"],"related_works":["https://openalex.org/W2349121885","https://openalex.org/W2089955609","https://openalex.org/W3111435437","https://openalex.org/W4298287745","https://openalex.org/W2039299714","https://openalex.org/W2094035517","https://openalex.org/W1983630542","https://openalex.org/W2949826017","https://openalex.org/W2065785067","https://openalex.org/W2012702868"],"abstract_inverted_index":{"Two":[0],"semi-implicit":[1,19],"Euler":[2,39,71],"schemes":[3,20],"for":[4,53],"differential":[5,27],"inclusions":[6,45],"are":[7,60],"proposed":[8],"and":[9],"analyzed":[10],"in":[11],"depth.":[12],"An":[13],"error":[14],"analysis":[15],"shows":[16],"that":[17,35],"both":[18],"inherit":[21],"favorable":[22],"stability":[23],"properties":[24],"from":[25],"the":[26,37,69],"inclusion.":[28],"Their":[29],"performance":[30],"is":[31],"considerably":[32],"better":[33],"than":[34,68],"of":[36,43],"implicit":[38,44,47,70],"scheme,":[40],"because":[41],"instead":[42],"only":[46],"equations":[48],"have":[49],"to":[50,65],"be":[51],"solved":[52],"computing":[54],"their":[55],"images.":[56],"In":[57],"addition,":[58],"they":[59],"more":[61],"robust":[62],"with":[63],"respect":[64],"spatial":[66],"discretization":[67],"scheme.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}