{"id":"https://openalex.org/W1999814105","doi":"https://doi.org/10.1145/1408800.1408837","title":"The efficient, scale-invariant determination of starting step sizes for high-order integrators","display_name":"The efficient, scale-invariant determination of starting step sizes for high-order integrators","publication_year":1974,"publication_date":"1974-01-01","ids":{"openalex":"https://openalex.org/W1999814105","doi":"https://doi.org/10.1145/1408800.1408837","mag":"1999814105"},"language":"en","primary_location":{"id":"doi:10.1145/1408800.1408837","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1408800.1408837","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 1974 annual conference on XX - ACM '74","raw_type":"proceedings-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/A5101659649","display_name":"David C. Williams","orcid":"https://orcid.org/0000-0002-6536-4038"},"institutions":[{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David C. Williams","raw_affiliation_strings":["Sandia Laboratories , Albuquerque , New Mexico"],"affiliations":[{"raw_affiliation_string":"Sandia Laboratories , Albuquerque , New Mexico","institution_ids":["https://openalex.org/I4210104735"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101659649"],"corresponding_institution_ids":["https://openalex.org/I4210104735"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13230241,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"501","last_page":"501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"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":0.9991999864578247,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T13286","display_name":"Modeling and Simulation Systems","score":0.9836000204086304,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.7833433151245117},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5284804105758667},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5088672637939453},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4737482964992523},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34576618671417236},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2888050675392151},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13484951853752136},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1257428526878357},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09165513515472412},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.08797293901443481},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.05989795923233032}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.7833433151245117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5284804105758667},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5088672637939453},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4737482964992523},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34576618671417236},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2888050675392151},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13484951853752136},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1257428526878357},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09165513515472412},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.08797293901443481},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.05989795923233032},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1408800.1408837","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1408800.1408837","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 1974 annual conference on XX - ACM '74","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1999312387","https://openalex.org/W2048610192","https://openalex.org/W3036935753"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2366352762","https://openalex.org/W2613964090","https://openalex.org/W2380425739","https://openalex.org/W2081322886","https://openalex.org/W2349324463","https://openalex.org/W1988313539","https://openalex.org/W2029980887","https://openalex.org/W2027541371"],"abstract_inverted_index":{"Many":[0],"routines":[1],"for":[2,35],"solving":[3],"differential":[4],"equations":[5],"require":[6],"the":[7,14,33,46,57,62,73,80,105,118,130],"user":[8,131],"to":[9,53,75,92],"specify":[10],"an":[11,24,126],"estimate":[12],"of":[13,22,48,59,61,77,86,138],"initial":[15],"step":[16,65,84],"size.":[17,66],"We":[18,112],"introduce":[19],"a":[20,114],"means":[21],"estimating":[23,56],"appropriate":[25,63],"value":[26],"automatically.":[27],"Strong":[28],"emphasis":[29],"is":[30],"placed":[31],"on":[32],"need":[34],"scale":[36,49,54,76],"invariance":[37],"in":[38,55,101],"making":[39],"such":[40,102],"estimates,":[41],"and":[42,50,89,124],"we":[43,70],"therefore":[44],"review":[45],"importance":[47],"matters":[51],"equivalent":[52],"order":[58],"magnitude":[60],"starting":[64],"In":[67],"this":[68,136],"context,":[69],"also":[71],"discuss":[72],"response":[74],"integrators":[78],"employing":[79],"error":[81,87],"per":[82],"unit":[83],"concept":[85],"control":[88],"are":[90,142],"forced":[91],"conclude":[93],"that":[94],"our":[95],"procedure":[96,119],"should":[97,107],"not":[98],"be":[99,108,121],"used":[100,109],"integrators,":[103],"if":[104],"latter":[106],"at":[110],"all.":[111],"note":[113],"special":[115],"case":[116],"where":[117],"could":[120],"badly":[122],"deceived":[123],"suggest":[125],"option":[127],"by":[128],"which":[129],"can":[132],"protect":[133],"himself":[134],"against":[135],"kind":[137],"mishap.":[139],"Test":[140],"results":[141],"cited.":[143]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
