{"id":"https://openalex.org/W2000463144","doi":"https://doi.org/10.1080/00207160802617012","title":"Numerical solution of homogeneous Smoluchowski's coagulation equation","display_name":"Numerical solution of homogeneous Smoluchowski's coagulation equation","publication_year":2009,"publication_date":"2009-10-20","ids":{"openalex":"https://openalex.org/W2000463144","doi":"https://doi.org/10.1080/00207160802617012","mag":"2000463144"},"language":"en","primary_location":{"id":"doi:10.1080/00207160802617012","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802617012","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/A5102017642","display_name":"Mojtaba Ranjbar","orcid":"https://orcid.org/0000-0001-9246-0650"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mojtaba Ranjbar","raw_affiliation_strings":["Faculty of Mathematics and Computer Sciences , Amirkabir University of Technology , Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Sciences , Amirkabir University of Technology , Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026886970","display_name":"Hojatollah Adibi","orcid":"https://orcid.org/0000-0002-8167-5020"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hojatollah Adibi","raw_affiliation_strings":["Faculty of Mathematics and Computer Sciences , Amirkabir University of Technology , Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Sciences , Amirkabir University of Technology , Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035058435","display_name":"Mehrdad Lakestani","orcid":"https://orcid.org/0000-0002-2752-0167"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mehrdad Lakestani","raw_affiliation_strings":["Faculty of Mathematical Science , University of Tabriz , Tabriz, Iran","Faculty of Mathematical science,#N#University of Tabriz, Tabriz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Science , University of Tabriz , Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]},{"raw_affiliation_string":"Faculty of Mathematical science,#N#University of Tabriz, Tabriz, Iran","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035058435"],"corresponding_institution_ids":["https://openalex.org/I41832843"],"apc_list":null,"apc_paid":null,"fwci":0.8852,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.80712204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"87","issue":"9","first_page":"2113","last_page":"2122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11188","display_name":"Coagulation and Flocculation Studies","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11188","display_name":"Coagulation and Flocculation Studies","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental 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":0.9289000034332275,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9077000021934509,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/smoluchowski-coagulation-equation","display_name":"Smoluchowski coagulation equation","score":0.958470344543457},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7349251508712769},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6003389358520508},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4797857403755188},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.47399604320526123},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46540695428848267},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4343022108078003},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4307840168476105},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4223124384880066},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.28685957193374634},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12068906426429749},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10851627588272095},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09859800338745117}],"concepts":[{"id":"https://openalex.org/C143002175","wikidata":"https://www.wikidata.org/wiki/Q971184","display_name":"Smoluchowski coagulation equation","level":2,"score":0.958470344543457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7349251508712769},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6003389358520508},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4797857403755188},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.47399604320526123},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46540695428848267},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4343022108078003},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4307840168476105},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4223124384880066},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.28685957193374634},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12068906426429749},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10851627588272095},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09859800338745117},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160802617012","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802617012","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"},{"id":"pmh:7b17b260-3f73-4930-b321-9480a81f8610","is_oa":false,"landing_page_url":"https://avesis.yyu.edu.tr/publication/details/7b17b260-3f73-4930-b321-9480a81f8610/oai","pdf_url":null,"source":{"id":"https://openalex.org/S7407055328","display_name":"Van Y\u00fcz\u00fcnc\u00fc Y\u0131l University Academic Data Management System","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W95329701","https://openalex.org/W165943075","https://openalex.org/W1572824337","https://openalex.org/W1964572025","https://openalex.org/W1966475838","https://openalex.org/W1966782416","https://openalex.org/W1976218309","https://openalex.org/W1980231741","https://openalex.org/W1994629223","https://openalex.org/W1997730282","https://openalex.org/W2008118419","https://openalex.org/W2010908535","https://openalex.org/W2017115674","https://openalex.org/W2026675047","https://openalex.org/W2030028087","https://openalex.org/W2052883156","https://openalex.org/W2057073325","https://openalex.org/W2062649642","https://openalex.org/W2064104303","https://openalex.org/W2067169069","https://openalex.org/W2072484564","https://openalex.org/W2091704124","https://openalex.org/W2095114434","https://openalex.org/W2095769364","https://openalex.org/W2101721214","https://openalex.org/W2121508168","https://openalex.org/W2137046381","https://openalex.org/W2164384292","https://openalex.org/W2166751846","https://openalex.org/W2167571677"],"related_works":["https://openalex.org/W2085079919","https://openalex.org/W2016101525","https://openalex.org/W2005392332","https://openalex.org/W2497704048","https://openalex.org/W2000463144","https://openalex.org/W1991762146","https://openalex.org/W2502890432","https://openalex.org/W2333659755","https://openalex.org/W2087968765","https://openalex.org/W1638304372"],"abstract_inverted_index":{"Smoluchowski's":[0,60,85],"equation":[1,62,86],"is":[2,52,106],"widely":[3],"applied":[4],"to":[5,37,40,78,87,108],"describe":[6,41],"the":[7,11,42,46,55,58,80,110,115],"time":[8,43],"evolution":[9,44],"of":[10,31,45,57,90,114],"cluster-size":[12,47],"distribution":[13],"during":[14],"aggregation":[15],"processes.":[16],"Analytical":[17],"solutions":[18],"for":[19,26,54,97],"this":[20,67],"equation,":[21],"however,":[22],"are":[23],"known":[24,104],"only":[25],"a":[27,88],"very":[28],"limited":[29],"number":[30],"kernels.":[32],"Therefore,":[33],"numerical":[34,50,101],"methods":[35],"have":[36],"be":[38,95],"used":[39],"distribution.":[48],"A":[49,100],"technique":[51],"presented":[53],"solution":[56,105],"homogeneous":[59],"coagulation":[61],"with":[63,103],"constant":[64],"kernel.":[65],"In":[66],"paper,":[68],"we":[69],"use":[70],"Taylor":[71],"polynomials":[72],"and":[73,112],"radial":[74],"basis":[75],"functions":[76],"together":[77],"solve":[79],"equation.":[81],"This":[82],"method":[83],"converts":[84],"system":[89],"nonlinear":[91],"equations":[92],"that":[93],"can":[94],"solved":[96],"unknown":[98],"parameters.":[99],"example":[102],"included":[107],"demonstrate":[109],"validity":[111],"applicability":[113],"technique.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}