{"id":"https://openalex.org/W2165853678","doi":"https://doi.org/10.1080/00207160008804923","title":"On one numerical method for solving some self-similarityproblems of gas-dynamics on a multiprocessor","display_name":"On one numerical method for solving some self-similarityproblems of gas-dynamics on a multiprocessor","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2165853678","doi":"https://doi.org/10.1080/00207160008804923","mag":"2165853678"},"language":"en","primary_location":{"id":"doi:10.1080/00207160008804923","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160008804923","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5061580345","display_name":"F. Criado","orcid":null},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"F. Criado","raw_affiliation_strings":["Department of Mathematics , M\u00e1laga University , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , M\u00e1laga University , Spain","institution_ids":["https://openalex.org/I82767444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007629118","display_name":"Tinatin Davitashvili","orcid":"https://orcid.org/0000-0001-6592-1095"},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"T. D. Davitashvili","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science , Tbilisi State University , Georgia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science , Tbilisi State University , Georgia","institution_ids":["https://openalex.org/I102808428"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082842686","display_name":"Hamlet Meladze","orcid":"https://orcid.org/0000-0002-7060-5457"},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"H. V. Meladze","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science , Tbilisi State University , Georgia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science , Tbilisi State University , Georgia","institution_ids":["https://openalex.org/I102808428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083935218","display_name":"N. M. Skhirtladze","orcid":null},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"N. M. Skhirtladze","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science , Tbilisi State University , Georgia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science , Tbilisi State University , Georgia","institution_ids":["https://openalex.org/I102808428"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.2318892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"74","issue":"1","first_page":"63","last_page":"85"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9603999853134155,"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":0.9603999853134155,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9603000283241272,"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/T13785","display_name":"Aquatic and Environmental Studies","score":0.960099995136261,"subfield":{"id":"https://openalex.org/subfields/1904","display_name":"Earth-Surface Processes"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7487267255783081},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6339196562767029},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5856909155845642},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5731619000434875},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48719877004623413},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4774251878261566},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4603024125099182},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.44599393010139465},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4410233199596405},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.274836927652359},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2470981776714325}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7487267255783081},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6339196562767029},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5856909155845642},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5731619000434875},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48719877004623413},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4774251878261566},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4603024125099182},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.44599393010139465},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4410233199596405},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.274836927652359},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2470981776714325},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160008804923","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160008804923","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W19209855","https://openalex.org/W1975400766","https://openalex.org/W2008336564","https://openalex.org/W2013348732","https://openalex.org/W2072043211","https://openalex.org/W3023930659","https://openalex.org/W3141390961","https://openalex.org/W6600804460","https://openalex.org/W6668602446","https://openalex.org/W7024430192"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W4288093367","https://openalex.org/W2059261580"],"abstract_inverted_index":{"In":[0],"this":[1,92,106],"paper":[2],"we":[3],"consider":[4],"mathematical":[5],"models":[6],"of":[7,10,17,24,37,56,71,76,91,99,105,116,122,127,133],"some":[8],"problems":[9,16,23,36],"natural":[11],"science,":[12],"for":[13,65,110],"example,":[14],"self-similarity":[15],"gas-dynamics":[18],"giving":[19],"rise":[20],"to":[21],"boundary":[22,35,68],"first":[25,38,73],"order":[26,39,74],"ordinary":[27],"differential":[28],"equations":[29],"(ODE)":[30],"with":[31,41,78],"one":[32,42,79,112],"parameter.":[33],"The":[34,89,103],"ODE":[40,77],"parameter":[43,80],"are":[44,59,143],"considered":[45],"in":[46,125,138],"[1,":[47],"2],":[48],"where":[49],"iterative":[50,63],"methods":[51],"based":[52],"on":[53,81],"the":[54,67,72,97,111,120,123,141],"implementation":[55],"Newton's":[57],"Method,":[58],"presented.":[60],"Next,":[61],"an":[62],"method":[64,107],"solving":[66],"value":[69],"problem":[70],"system":[75],"a":[82,128],"multiprocessor":[83],"type":[84],"SIMD":[85],"[3]":[86],"is":[87,94,101,108],"shown.":[88],"convergence":[90,100],"process":[93],"proved":[95],"and":[96,136],"speed":[98],"estimated.":[102],"feasibility":[104],"illustrated":[109],"dimensional":[113],"instability":[114],"movement":[115,121],"gas":[117],"arising":[118],"from":[119],"piston":[124],"presence":[126],"volume":[129],"source":[130],"(volume":[131],"channel)":[132],"mass,":[134],"impulse":[135],"energy":[137],"gas.":[139],"Finally":[140],"results":[142],"given.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}