{"id":"https://openalex.org/W4327860905","doi":"https://doi.org/10.1080/00207160.2023.2192304","title":"Using 2D and 1D block-pulse functions simultaneously for solving the Barbashin integro-differential equations","display_name":"Using 2D and 1D block-pulse functions simultaneously for solving the Barbashin integro-differential equations","publication_year":2023,"publication_date":"2023-03-19","ids":{"openalex":"https://openalex.org/W4327860905","doi":"https://doi.org/10.1080/00207160.2023.2192304"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2023.2192304","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207160.2023.2192304","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/A5090593583","display_name":"S. Akhavan","orcid":"https://orcid.org/0000-0002-0426-0438"},"institutions":[{"id":"https://openalex.org/I2799360687","display_name":"Islamic Azad University of Khomeynishahr","ror":"https://ror.org/01qskrs45","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I2799360687"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"S. Akhavan","raw_affiliation_strings":["Department of Mathematics, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran","institution_ids":["https://openalex.org/I2799360687"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029014615","display_name":"A. Roohollahi","orcid":null},"institutions":[{"id":"https://openalex.org/I2799360687","display_name":"Islamic Azad University of Khomeynishahr","ror":"https://ror.org/01qskrs45","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I2799360687"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"A. Roohollahi","raw_affiliation_strings":["Department of Mathematics, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran","institution_ids":["https://openalex.org/I2799360687"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090593583"],"corresponding_institution_ids":["https://openalex.org/I2799360687"],"apc_list":null,"apc_paid":null,"fwci":0.2242,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.44679885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"100","issue":"10","first_page":"1957","last_page":"1970"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9984999895095825,"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":0.9965000152587891,"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/volterra-integral-equation","display_name":"Volterra integral equation","score":0.7793731689453125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7330461144447327},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.6303560733795166},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6057273149490356},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5925848484039307},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5406489372253418},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.5293135046958923},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5044347047805786},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48629388213157654},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.45997026562690735},{"id":"https://openalex.org/keywords/integro-differential-equation","display_name":"Integro-differential equation","score":0.4556778073310852},{"id":"https://openalex.org/keywords/pulse","display_name":"Pulse (music)","score":0.4303331971168518},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4184708595275879},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33845070004463196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24652254581451416},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.21734532713890076},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.12880703806877136}],"concepts":[{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.7793731689453125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7330461144447327},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.6303560733795166},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6057273149490356},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5925848484039307},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5406489372253418},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.5293135046958923},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5044347047805786},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48629388213157654},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.45997026562690735},{"id":"https://openalex.org/C70985411","wikidata":"https://www.wikidata.org/wiki/Q2380676","display_name":"Integro-differential equation","level":4,"score":0.4556778073310852},{"id":"https://openalex.org/C2780167933","wikidata":"https://www.wikidata.org/wiki/Q1550652","display_name":"Pulse (music)","level":3,"score":0.4303331971168518},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4184708595275879},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33845070004463196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24652254581451416},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.21734532713890076},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.12880703806877136},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical 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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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:10.1080/00207160.2023.2192304","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207160.2023.2192304","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W608708317","https://openalex.org/W626109261","https://openalex.org/W1567668233","https://openalex.org/W2004733573","https://openalex.org/W2009505914","https://openalex.org/W2012343919","https://openalex.org/W2029153938","https://openalex.org/W2029302017","https://openalex.org/W2043173125","https://openalex.org/W2046659499","https://openalex.org/W2047833018","https://openalex.org/W2063454774","https://openalex.org/W2082464798","https://openalex.org/W2099290207","https://openalex.org/W2224652591","https://openalex.org/W2590352016","https://openalex.org/W2890031009","https://openalex.org/W3007342316","https://openalex.org/W3140172803","https://openalex.org/W4292750136"],"related_works":["https://openalex.org/W1541040149","https://openalex.org/W1539637428","https://openalex.org/W4367557662","https://openalex.org/W2118560105","https://openalex.org/W2517687681","https://openalex.org/W2906624979","https://openalex.org/W4240464390","https://openalex.org/W3200459157","https://openalex.org/W3097583914","https://openalex.org/W2048886917"],"abstract_inverted_index":{"AbstractThe":[0],"goal":[1],"of":[2,17,105,121],"this":[3,42,58],"work":[4],"is":[5,63,84],"to":[6,10,40,65],"look":[7],"at":[8],"how":[9],"solve":[11,41],"Barbashin":[12,61],"equations":[13,20],"using":[14,73],"a":[15,37,49,66],"mix":[16],"Volterra\u2013Fredholm":[18],"integro-differential":[19],"and":[21,30],"Volterra":[22],"equations.":[23],"For":[24],"the":[25,28,53,97,101,126],"first":[26],"time,":[27],"1D":[29],"2D":[31],"block-pulse":[32],"functions":[33],"are":[34,94],"employed":[35],"in":[36,96],"hybrid":[38],"technique":[39],"two-dimensional":[43],"integral":[44,115],"problem":[45],"concurrently.":[46],"We":[47],"construct":[48],"new":[50],"matrix":[51,56],"called":[52],"converter":[54],"operating":[55],"for":[57],"purpose.":[59],"The":[60,79],"equation":[62,116],"reduced":[64],"linear":[67],"system":[68],"that":[69],"can":[70],"be":[71],"solved":[72],"well-known":[74],"methods":[75],"employing":[76],"direct":[77],"computing.":[78],"proposed":[80],"method's":[81],"convergence":[82],"theorem":[83],"demonstrated":[85],"under":[86],"appropriate":[87],"conditions.":[88],"In":[89],"addition,":[90],"some":[91],"numerical":[92],"results":[93],"presented":[95],"paper,":[98],"which":[99],"supports":[100],"strong":[102],"theoretical":[103],"properties":[104],"our":[106],"approach.Keywords:":[107],"Mixed":[108],"Volterra-FredholmBarbashin":[109],"equationoperational":[110],"matricesconverter":[111],"operational":[112],"matrixintegro-differential":[113],"equationspartial":[114],"Disclosure":[117],"statementNo":[118],"potential":[119],"conflict":[120],"interest":[122],"was":[123],"reported":[124],"by":[125],"author(s).":[127]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-22T23:10:17.713674","created_date":"2025-10-10T00:00:00"}
