{"id":"https://openalex.org/W1983626329","doi":"https://doi.org/10.1145/1479064.1479144","title":"On the hybrid computer solution of partial differential equations with two spatial dimensions","display_name":"On the hybrid computer solution of partial differential equations with two spatial dimensions","publication_year":1971,"publication_date":"1971-01-01","ids":{"openalex":"https://openalex.org/W1983626329","doi":"https://doi.org/10.1145/1479064.1479144","mag":"1983626329"},"language":"en","primary_location":{"id":"doi:10.1145/1479064.1479144","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1479064.1479144","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1479064.1479144","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the May 16-18, 1972, spring joint computer conference on - AFIPS '72 (Spring)","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/10.1145/1479064.1479144","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002162282","display_name":"George A. Bekey","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George A. Bekey","raw_affiliation_strings":["University of Southern California, Los Angeles, California","University of Southern California, Los Angeles, California;"],"affiliations":[{"raw_affiliation_string":"University of Southern California, Los Angeles, California","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"University of Southern California, Los Angeles, California;","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029228696","display_name":"Man T. Ung","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Man T. Ung","raw_affiliation_strings":["Dillingham Environmental Company, La Jolla, California"],"affiliations":[{"raw_affiliation_string":"Dillingham Environmental Company, La Jolla, California","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002162282"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":0.5397,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59428895,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"401","last_page":"401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.996999979019165,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9969000220298767,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9962999820709229,"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/dimension","display_name":"Dimension (graph theory)","score":0.7269337773323059},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.695472776889801},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6792948246002197},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6504655480384827},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5419491529464722},{"id":"https://openalex.org/keywords/analog-computer","display_name":"Analog computer","score":0.4938846230506897},{"id":"https://openalex.org/keywords/exponential-integrator","display_name":"Exponential integrator","score":0.4337945580482483},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4322557747364044},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41403326392173767},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3799918293952942},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35707390308380127},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.33474618196487427},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.326999306678772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32018911838531494},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15328556299209595},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.14450183510780334}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7269337773323059},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.695472776889801},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6792948246002197},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6504655480384827},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5419491529464722},{"id":"https://openalex.org/C90915687","wikidata":"https://www.wikidata.org/wiki/Q63759","display_name":"Analog computer","level":2,"score":0.4938846230506897},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.4337945580482483},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4322557747364044},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41403326392173767},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3799918293952942},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35707390308380127},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.33474618196487427},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.326999306678772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32018911838531494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15328556299209595},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.14450183510780334},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1479064.1479144","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1479064.1479144","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1479064.1479144","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the May 16-18, 1972, spring joint computer conference on - AFIPS '72 (Spring)","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/1479064.1479144","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1479064.1479144","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1479064.1479144","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the May 16-18, 1972, spring joint computer conference on - AFIPS '72 (Spring)","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1983626329.pdf","grobid_xml":"https://content.openalex.org/works/W1983626329.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1984794436","https://openalex.org/W1989820565","https://openalex.org/W2030234544","https://openalex.org/W2043857934","https://openalex.org/W2052487727","https://openalex.org/W2053262745","https://openalex.org/W2056297183","https://openalex.org/W2095036901","https://openalex.org/W2143674133","https://openalex.org/W2150424620"],"related_works":["https://openalex.org/W2999616507","https://openalex.org/W4392238179","https://openalex.org/W3146600122","https://openalex.org/W77016536","https://openalex.org/W2029287765","https://openalex.org/W2043671984","https://openalex.org/W2979449540","https://openalex.org/W2020046414","https://openalex.org/W1979864573","https://openalex.org/W2108370162"],"abstract_inverted_index":{"For":[0],"a":[1],"number":[2],"of":[3,11,15,25,33,43,61,85],"years":[4],"it":[5,48],"has":[6,68],"been":[7],"suggested":[8],"that":[9],"one":[10,75],"the":[12,23,31,38,62,66,81,86],"fruitful":[13],"areas":[14],"application":[16],"for":[17],"hybrid":[18],"computation":[19],"might":[20],"lie":[21],"in":[22,65,74],"study":[24],"distributed":[26],"parameter":[27],"systems.":[28],"In":[29],"principle,":[30],"combination":[32],"analog":[34],"computer":[35],"speed":[36],"with":[37,71],"memory":[39],"and":[40,57,78,83],"logical":[41],"capabilities":[42],"digital":[44],"machines":[45],"should":[46],"make":[47],"possible":[49],"to":[50],"solve":[51],"partial":[52],"differential":[53],"equations":[54],"both":[55],"efficiently":[56],"rapidly.":[58],"However,":[59],"most":[60],"published":[63],"work":[64],"field":[67],"dealt":[69],"only":[70],"linear":[72],"problems":[73],"spatial":[76],"dimension":[77],"time,":[79],"where":[80],"advantages":[82],"limitations":[84],"particular":[87],"methods":[88],"do":[89],"not":[90],"stand":[91],"out":[92],"clearly.":[93]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}