{"id":"https://openalex.org/W2033468195","doi":"https://doi.org/10.1145/1499799.1499932","title":"System theoretic implications of numerical methods applied to the solution of ordinary differential equations","display_name":"System theoretic implications of numerical methods applied to the solution of ordinary differential equations","publication_year":1976,"publication_date":"1976-01-01","ids":{"openalex":"https://openalex.org/W2033468195","doi":"https://doi.org/10.1145/1499799.1499932","mag":"2033468195"},"language":"en","primary_location":{"id":"doi:10.1145/1499799.1499932","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1499799.1499932","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1499799.1499932","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the June 7-10, 1976, national computer conference and exposition on - AFIPS '76","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/1499799.1499932","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024850326","display_name":"T. G. Windeknecht","orcid":null},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"T. G. Windeknecht","raw_affiliation_strings":["Memphis State University, Memphis, Tennessee"],"affiliations":[{"raw_affiliation_string":"Memphis State University, Memphis, Tennessee","institution_ids":["https://openalex.org/I94658018"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019955455","display_name":"Henry D'Angelo","orcid":null},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. D'angelo","raw_affiliation_strings":["Memphis State University, Memphis, Tennessee"],"affiliations":[{"raw_affiliation_string":"Memphis State University, Memphis, Tennessee","institution_ids":["https://openalex.org/I94658018"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024850326"],"corresponding_institution_ids":["https://openalex.org/I94658018"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.17067109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"963","last_page":"963"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9965999722480774,"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":0.9965999722480774,"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/T13286","display_name":"Modeling and Simulation Systems","score":0.989300012588501,"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/T12810","display_name":"Real-time simulation and control systems","score":0.972000002861023,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-integrator","display_name":"Exponential integrator","score":0.6699255704879761},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.6496968865394592},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6439070105552673},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5919400453567505},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5899175405502319},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5637047290802002},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5340762138366699},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.5166087746620178},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.45481738448143005},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.4536229968070984},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.45335426926612854},{"id":"https://openalex.org/keywords/block-diagram","display_name":"Block diagram","score":0.4412330389022827},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.42071881890296936},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41216135025024414},{"id":"https://openalex.org/keywords/integrating-factor","display_name":"Integrating factor","score":0.41106194257736206},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.35765933990478516},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33162665367126465},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.3165770173072815},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2999902665615082},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0819104015827179},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06211647391319275}],"concepts":[{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.6699255704879761},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.6496968865394592},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6439070105552673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5919400453567505},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5899175405502319},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5637047290802002},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5340762138366699},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.5166087746620178},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.45481738448143005},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.4536229968070984},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.45335426926612854},{"id":"https://openalex.org/C149227320","wikidata":"https://www.wikidata.org/wiki/Q884718","display_name":"Block diagram","level":2,"score":0.4412330389022827},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.42071881890296936},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41216135025024414},{"id":"https://openalex.org/C163105828","wikidata":"https://www.wikidata.org/wiki/Q2734005","display_name":"Integrating factor","level":5,"score":0.41106194257736206},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.35765933990478516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33162665367126465},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.3165770173072815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2999902665615082},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0819104015827179},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06211647391319275},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1499799.1499932","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1499799.1499932","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1499799.1499932","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the June 7-10, 1976, national computer conference and exposition on - AFIPS '76","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/1499799.1499932","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1499799.1499932","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1499799.1499932","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the June 7-10, 1976, national computer conference and exposition on - AFIPS '76","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2033468195.pdf","grobid_xml":"https://content.openalex.org/works/W2033468195.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2058984211","https://openalex.org/W6601528769","https://openalex.org/W6814547148"],"related_works":["https://openalex.org/W2340807170","https://openalex.org/W185970870","https://openalex.org/W1983755086","https://openalex.org/W823974124","https://openalex.org/W2383059892","https://openalex.org/W145033235","https://openalex.org/W4292934066","https://openalex.org/W4320000718","https://openalex.org/W606479956","https://openalex.org/W2240393724"],"abstract_inverted_index":{"This":[0],"paper":[1,76],"presents":[2],"a":[3,33,40,47],"system-theoretic":[4,126],"analysis":[5,157],"of":[6,13,28,46,64,66,74,130,132,149,158],"numerical":[7,34,137,152],"methods":[8,138,153],"used":[9,99,136],"in":[10,42,154],"approximating":[11],"solutions":[12],"ordinary":[14,19],"differential":[15,20,88],"equations.":[16,124],"By":[17],"representing":[18],"equations":[21],"with":[22],"system":[23,49,81,117],"block":[24,82],"diagrams":[25],"(i.e.,":[26,58],"interconnections":[27,65],"static":[29,67,92,106,110],"elements":[30,68],"and":[31,69,94,108,143,146],"integrators),":[32],"method":[35],"can":[36,118],"be":[37,119],"viewed":[38],"as":[39],"process":[41],"which":[43],"the":[44,56,75,80,86,96,102,114,133,147,155],"integrators":[45,57,103],"continuous":[48],"are":[50,161],"replaced":[51],"by":[52,59,121],"discrete":[53,60,97,116],"approximations":[54],"to":[55,85,100],"subsystems":[61,98],"made":[62],"up":[63],"delays).":[70],"The":[71],"main":[72],"result":[73],"establishes":[77],"that":[78],"if":[79,95],"diagram":[83],"corresponding":[84],"original":[87],"equation":[89],"has":[90],"no":[91,105,109],"loops":[93,107],"replace":[101],"have":[104],"through":[111],"paths,":[112],"then":[113],"resulting":[115],"characterized":[120],"explicit":[122],"difference":[123],"A":[125],"study":[127],"is":[128],"conducted":[129],"several":[131],"more":[134],"commonly":[135],"(the":[139],"Euler,":[140],"trapezoidal,":[141],"Runge-Kutta,":[142],"predictor-corrector":[144],"methods)":[145],"limitations":[148],"using":[150],"these":[151],"real-time":[156],"input-output":[159],"systems":[160],"examined.":[162]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
