{"id":"https://openalex.org/W4319225915","doi":"https://doi.org/10.1007/s00211-023-01344-0","title":"Rate of convergence and stability analysis of a modified fixed pivot technique for a fragmentation equation","display_name":"Rate of convergence and stability analysis of a modified fixed pivot technique for a fragmentation equation","publication_year":2023,"publication_date":"2023-02-04","ids":{"openalex":"https://openalex.org/W4319225915","doi":"https://doi.org/10.1007/s00211-023-01344-0"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-023-01344-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01344-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01344-0.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01344-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004215041","display_name":"Jitraj Saha","orcid":"https://orcid.org/0000-0002-8864-5537"},"institutions":[{"id":"https://openalex.org/I122964287","display_name":"National Institute of Technology Tiruchirappalli","ror":"https://ror.org/047x65e68","country_code":"IN","type":"education","lineage":["https://openalex.org/I122964287"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jitraj Saha","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli, Tamil Nadu, 620 015, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli, Tamil Nadu, 620 015, India","institution_ids":["https://openalex.org/I122964287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001129409","display_name":"Mehakpreet Singh","orcid":"https://orcid.org/0000-0002-6392-6068"},"institutions":[{"id":"https://openalex.org/I230495080","display_name":"University of Limerick","ror":"https://ror.org/00a0n9e72","country_code":"IE","type":"education","lineage":["https://openalex.org/I230495080"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Mehakpreet Singh","raw_affiliation_strings":["Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland"],"affiliations":[{"raw_affiliation_string":"Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, V94 T9PX, Ireland","institution_ids":["https://openalex.org/I230495080"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001129409"],"corresponding_institution_ids":["https://openalex.org/I230495080"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.86,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83194539,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"153","issue":"2-3","first_page":"531","last_page":"555"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11188","display_name":"Coagulation and Flocculation Studies","score":0.9973999857902527,"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":0.9973999857902527,"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/T12540","display_name":"Cyclone Separators and Fluid Dynamics","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12350","display_name":"Particle Dynamics in Fluid Flows","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/mathematics","display_name":"Mathematics","score":0.7682400941848755},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6887900829315186},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5278316140174866},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.49825119972229004},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4897458553314209},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.45210903882980347},{"id":"https://openalex.org/keywords/breakup","display_name":"Breakup","score":0.43532803654670715},{"id":"https://openalex.org/keywords/convergence-tests","display_name":"Convergence tests","score":0.4175333082675934},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35681843757629395},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09804219007492065},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08411037921905518},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.07556071877479553}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7682400941848755},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6887900829315186},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5278316140174866},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.49825119972229004},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4897458553314209},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.45210903882980347},{"id":"https://openalex.org/C2777871205","wikidata":"https://www.wikidata.org/wiki/Q100926628","display_name":"Breakup","level":2,"score":0.43532803654670715},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.4175333082675934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35681843757629395},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09804219007492065},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08411037921905518},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.07556071877479553},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-023-01344-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01344-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01344-0.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/22182193","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Rate_of_convergence_and_stability_analysis_of_a_modified_fixed_pivot_technique_for_a_fragmentation_equation/22182193","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.34961/researchrepository-ul.22182193.v1","is_oa":true,"landing_page_url":"https://doi.org/10.34961/researchrepository-ul.22182193.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401529","display_name":"University of Limerick Institutional Repository (University of Limerick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I230495080","host_organization_name":"University of Limerick","host_organization_lineage":["https://openalex.org/I230495080"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s00211-023-01344-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01344-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01344-0.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320318630","display_name":"Irish Research eLibrary","ror":null},{"id":"https://openalex.org/F4320320862","display_name":"University of Limerick","ror":"https://ror.org/00a0n9e72"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4319225915.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W927674661","https://openalex.org/W1968447685","https://openalex.org/W1969713947","https://openalex.org/W1974051064","https://openalex.org/W2023760604","https://openalex.org/W2051722183","https://openalex.org/W2059229412","https://openalex.org/W2068083743","https://openalex.org/W2072484564","https://openalex.org/W2124966449","https://openalex.org/W2165520457","https://openalex.org/W2327646289","https://openalex.org/W2552970272","https://openalex.org/W2792931744","https://openalex.org/W2885859055","https://openalex.org/W2943892683","https://openalex.org/W2987807107","https://openalex.org/W3025420353","https://openalex.org/W3096599988","https://openalex.org/W3135098670","https://openalex.org/W3161085569","https://openalex.org/W4220761728","https://openalex.org/W4223570782","https://openalex.org/W4234429411","https://openalex.org/W4249613604","https://openalex.org/W4281893635","https://openalex.org/W4290785841","https://openalex.org/W4294287012","https://openalex.org/W6632295984"],"related_works":["https://openalex.org/W2180233726","https://openalex.org/W2551580799","https://openalex.org/W2484170550","https://openalex.org/W2058880726","https://openalex.org/W52475494","https://openalex.org/W3150825038","https://openalex.org/W3028403277","https://openalex.org/W2152293383","https://openalex.org/W2893613551","https://openalex.org/W2171761037"],"abstract_inverted_index":{"Abstract":[0],"This":[1,104,129],"study":[2],"presents":[3],"the":[4,40,44,49,55,60,64,77,94,106,111,125,133,136,149,166,171,180],"convergence":[5,123,175],"and":[6,53,84,101,109,120,141,148,154,170],"stability":[7],"analysis":[8],"of":[9,39,51,98,124,132,174,183],"a":[10,72,82,85,99],"recently":[11],"developed":[12],"fixed":[13,137],"pivot":[14,138],"technique":[15,139,152,169],"for":[16,115],"fragmentation":[17],"equations":[18],"(Liao":[19],"et":[20],"al.":[21],"in":[22,63,71,143,156],"Int":[23],"J":[24],"Numer":[25,144,157],"Methods":[26],"Fluids":[27],"87(4):202\u2013215,":[28],"2018).":[29],"The":[30,66,118],"approach":[31],"is":[32,176],"based":[33],"on":[34],"preserving":[35],"two":[36],"integral":[37],"moments":[38],"distribution,":[41],"namely":[42],"(a)":[43],"zeroth-order":[45],"moment,":[46,57],"which":[47,58],"defines":[48],"number":[50],"particles,":[52],"(b)":[54],"first-order":[56],"describes":[59],"total":[61,78],"mass":[62],"system.":[65],"present":[67],"methodology":[68],"differs":[69],"mathematically":[70],"way":[73],"that":[74],"it":[75],"delivers":[76],"breakage":[79],"rate":[80,97],"between":[81],"mother":[83,100],"daughter":[86,102],"particle":[87],"immediately,":[88],"whereas":[89],"existing":[90],"numerical":[91],"techniques":[92],"provide":[93],"partial":[95],"breakup":[96],"particle.":[103],"affects":[105],"computational":[107],"efficiency":[108,131],"makes":[110],"current":[112],"model":[113],"reliable":[114],"CFD":[116],"simulations.":[117],"consistency":[119],"unconditional":[121],"second-order":[122],"method":[126,134],"are":[127,163],"proved.":[128],"demonstrates":[130],"over":[135],"(Kumar":[140,153],"Warnecke":[142,155],"Math":[145,158],"110(4):539\u2013559,":[146],"2008)":[147],"cell":[150,167],"average":[151,168],"111(1):81\u2013108,":[159],"2008).":[160],"Numerical":[161],"results":[162],"compared":[164],"against":[165],"experimental":[172],"order":[173,182],"calculated":[177],"to":[178],"confirm":[179],"theoretical":[181],"convergence.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}