{"id":"https://openalex.org/W7130408164","doi":"https://doi.org/10.1016/j.jocs.2026.102813","title":"Non-linear collision-induced breakage equation: Approximate solution and error estimation","display_name":"Non-linear collision-induced breakage equation: Approximate solution and error estimation","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130408164","doi":"https://doi.org/10.1016/j.jocs.2026.102813"},"language":"en","primary_location":{"id":"doi:10.1016/j.jocs.2026.102813","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jocs.2026.102813","pdf_url":null,"source":{"id":"https://openalex.org/S192071280","display_name":"Journal of Computational Science","issn_l":"1877-7503","issn":["1877-7503","1877-7511"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Science","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/A5057334294","display_name":"Sanjiv Kumar Bariwal","orcid":"https://orcid.org/0009-0007-0919-0188"},"institutions":[{"id":"https://openalex.org/I74796645","display_name":"Birla Institute of Technology and Science, Pilani","ror":"https://ror.org/001p3jz28","country_code":"IN","type":"education","lineage":["https://openalex.org/I74796645"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sanjiv Kumar Bariwal","raw_affiliation_strings":["Department of Mathematics, Birla Institute of Technology and Science, Pilani, Pilani 333031, Rajasthan, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Birla Institute of Technology and Science, Pilani, Pilani 333031, Rajasthan, India","institution_ids":["https://openalex.org/I74796645"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126333831","display_name":"Rajesh Kumar","orcid":null},"institutions":[{"id":"https://openalex.org/I74796645","display_name":"Birla Institute of Technology and Science, Pilani","ror":"https://ror.org/001p3jz28","country_code":"IN","type":"education","lineage":["https://openalex.org/I74796645"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rajesh Kumar","raw_affiliation_strings":["Department of Mathematics, Birla Institute of Technology and Science, Pilani, Pilani 333031, Rajasthan, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Birla Institute of Technology and Science, Pilani, Pilani 333031, Rajasthan, India","institution_ids":["https://openalex.org/I74796645"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057334294"],"corresponding_institution_ids":["https://openalex.org/I74796645"],"apc_list":{"value":2810,"currency":"USD","value_usd":2810},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.63619964,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":null,"first_page":"102813","last_page":"102813"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.4187000095844269,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.4187000095844269,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11188","display_name":"Coagulation and Flocculation Studies","score":0.21240000426769257,"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/T11603","display_name":"Dust and Plasma Wave Phenomena","score":0.10830000042915344,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/breakage","display_name":"Breakage","score":0.8008999824523926},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.644599974155426},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6062999963760376},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.5486000180244446},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4681999981403351},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.44519999623298645},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44190001487731934},{"id":"https://openalex.org/keywords/error-function","display_name":"Error function","score":0.4302000105381012},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4043999910354614}],"concepts":[{"id":"https://openalex.org/C2779015675","wikidata":"https://www.wikidata.org/wiki/Q92796261","display_name":"Breakage","level":2,"score":0.8008999824523926},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6503999829292297},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.644599974155426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6100000143051147},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6062999963760376},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.5486000180244446},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4681999981403351},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44190001487731934},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.4302000105381012},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.364300012588501},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.35530000925064087},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.3257000148296356},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3019999861717224},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3009999990463257},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jocs.2026.102813","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jocs.2026.102813","pdf_url":null,"source":{"id":"https://openalex.org/S192071280","display_name":"Journal of Computational Science","issn_l":"1877-7503","issn":["1877-7503","1877-7511"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Science","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":37,"referenced_works":["https://openalex.org/W927674661","https://openalex.org/W1966941542","https://openalex.org/W1968447685","https://openalex.org/W1969202999","https://openalex.org/W1975321722","https://openalex.org/W2000293971","https://openalex.org/W2020658528","https://openalex.org/W2025326085","https://openalex.org/W2033816084","https://openalex.org/W2038137143","https://openalex.org/W2042679449","https://openalex.org/W2059229412","https://openalex.org/W2072203466","https://openalex.org/W2073607859","https://openalex.org/W2075416456","https://openalex.org/W2081587196","https://openalex.org/W2082927006","https://openalex.org/W2085907930","https://openalex.org/W2124966449","https://openalex.org/W2146486351","https://openalex.org/W2160031808","https://openalex.org/W2321788680","https://openalex.org/W2781064445","https://openalex.org/W2903769531","https://openalex.org/W2962879612","https://openalex.org/W2963955044","https://openalex.org/W2963962235","https://openalex.org/W2982423483","https://openalex.org/W3018466582","https://openalex.org/W3112962829","https://openalex.org/W3128287227","https://openalex.org/W3195290736","https://openalex.org/W4210697094","https://openalex.org/W4292155149","https://openalex.org/W4294308879","https://openalex.org/W4389215433","https://openalex.org/W4398616693"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-02-21T06:11:54.161237","created_date":"2026-02-19T00:00:00"}