{"id":"https://openalex.org/W2053307571","doi":"https://doi.org/10.1515/jnum-2012-0006","title":"A note on the stability of the upwind scheme for ordinary differential equations","display_name":"A note on the stability of the upwind scheme for ordinary differential equations","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2053307571","doi":"https://doi.org/10.1515/jnum-2012-0006","mag":"2053307571"},"language":"en","primary_location":{"id":"doi:10.1515/jnum-2012-0006","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnum-2012-0006","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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/A5112094949","display_name":"H.-J. Reinhardt","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"H. J. Reinhardt","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112094949"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.13256228,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","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/T12727","display_name":"Differential Equations and Numerical Methods","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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9926999807357788,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9919000267982483,"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/mathematics","display_name":"Mathematics","score":0.8813749551773071},{"id":"https://openalex.org/keywords/upwind-scheme","display_name":"Upwind scheme","score":0.7986158132553101},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.733884334564209},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5263662934303284},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.49540603160858154},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.42658472061157227},{"id":"https://openalex.org/keywords/exact-differential-equation","display_name":"Exact differential equation","score":0.41018858551979065},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4057499170303345},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40021541714668274},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.08543384075164795},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07305508852005005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8813749551773071},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.7986158132553101},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.733884334564209},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5263662934303284},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49540603160858154},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.42658472061157227},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.41018858551979065},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4057499170303345},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40021541714668274},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.08543384075164795},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07305508852005005},{"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:10.1515/jnum-2012-0006","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnum-2012-0006","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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":14,"referenced_works":["https://openalex.org/W79873316","https://openalex.org/W314286854","https://openalex.org/W572560280","https://openalex.org/W638725251","https://openalex.org/W1480673526","https://openalex.org/W1583880678","https://openalex.org/W1586230637","https://openalex.org/W1977135416","https://openalex.org/W2018032381","https://openalex.org/W2079779150","https://openalex.org/W2152425443","https://openalex.org/W2587287691","https://openalex.org/W2770823503","https://openalex.org/W2915870397"],"related_works":["https://openalex.org/W2363102870","https://openalex.org/W2362647453","https://openalex.org/W2486405686","https://openalex.org/W4387498025","https://openalex.org/W82452836","https://openalex.org/W2145770879","https://openalex.org/W2143046811","https://openalex.org/W191904733","https://openalex.org/W1833008280","https://openalex.org/W2370760654"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"the":[3,6,21,42,45,48,62],"stability":[4],"of":[5,20,44,47],"upwind":[7],"scheme":[8],"for":[9],"second":[10],"order,":[11],"linear":[12],"ordinary":[13],"differential":[14,49],"equations":[15],"with":[16],"general":[17],"boundary":[18],"conditions":[19],"third":[22],"kind":[23],"is":[24,28,35,52],"proved.":[25],"The":[26],"proof":[27],"carried":[29],"out":[30],"via":[31],"compactness":[32],"arguments":[33],"and":[34],"rather":[36],"short.":[37],"Moreover,":[38],"no":[39],"information":[40],"on":[41],"behaviour":[43],"solution":[46],"equation":[50],"itself":[51],"needed.":[53],"This":[54],"approach":[55],"seems":[56],"not":[57],"to":[58],"be":[59],"present":[60],"in":[61],"existing":[63],"literature.":[64]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
