{"id":"https://openalex.org/W2614366477","doi":"https://doi.org/10.3846/13926292.2017.1313329","title":"NUMERICAL STUDY OF ROSENAU-KDV EQUATION USING FINITE ELEMENT METHOD BASED ON COLLOCATION APPROACH","display_name":"NUMERICAL STUDY OF ROSENAU-KDV EQUATION USING FINITE ELEMENT METHOD BASED ON COLLOCATION APPROACH","publication_year":2017,"publication_date":"2017-05-19","ids":{"openalex":"https://openalex.org/W2614366477","doi":"https://doi.org/10.3846/13926292.2017.1313329","mag":"2614366477"},"language":"en","primary_location":{"id":"doi:10.3846/13926292.2017.1313329","is_oa":true,"landing_page_url":"https://doi.org/10.3846/13926292.2017.1313329","pdf_url":"https://journals.vgtu.lt/index.php/MMA/article/download/902/682","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journals.vgtu.lt/index.php/MMA/article/download/902/682","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031191833","display_name":"Turgut Ak","orcid":"https://orcid.org/0000-0001-8368-8506"},"institutions":[{"id":"https://openalex.org/I40790370","display_name":"Yalova University","ror":"https://ror.org/01x18ax09","country_code":"TR","type":"education","lineage":["https://openalex.org/I40790370"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Turgut Ak","raw_affiliation_strings":["Yalova University","Department of Transportation Engineering, Yalova University, 77100 Yalova, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yalova University","institution_ids":["https://openalex.org/I40790370"]},{"raw_affiliation_string":"Department of Transportation Engineering, Yalova University, 77100 Yalova, Turkey","institution_ids":["https://openalex.org/I40790370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073337370","display_name":"Sharanjeet Dhawan","orcid":"https://orcid.org/0000-0003-2970-0169"},"institutions":[{"id":"https://openalex.org/I4210133503","display_name":"Central University of Haryana","ror":"https://ror.org/03mtwkv54","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210133503"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sharanjeet Dhawan","raw_affiliation_strings":["Central University of Haryana","Department of Mathematics, Central University of Haryana, 123029 Haryana, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Central University of Haryana","institution_ids":["https://openalex.org/I4210133503"]},{"raw_affiliation_string":"Department of Mathematics, Central University of Haryana, 123029 Haryana, India","institution_ids":["https://openalex.org/I4210133503"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086563926","display_name":"Seydi Battal Gazi Karako\u00e7","orcid":"https://orcid.org/0000-0002-2348-4170"},"institutions":[{"id":"https://openalex.org/I1281109512","display_name":"Nev\u015fehir Hac\u0131 Bekta\u015f Veli University","ror":"https://ror.org/019jds967","country_code":"TR","type":"education","lineage":["https://openalex.org/I1281109512"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"S. Battal Gazi Karakoc","raw_affiliation_strings":["Nevsehir Haci Bektas Veli University","Department of Mathematics, Nevsehir Haci Bektas Veli University, 50300 Nevsehir, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nevsehir Haci Bektas Veli University","institution_ids":["https://openalex.org/I1281109512"]},{"raw_affiliation_string":"Department of Mathematics, Nevsehir Haci Bektas Veli University, 50300 Nevsehir, Turkey","institution_ids":["https://openalex.org/I1281109512"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035803549","display_name":"Samir Kumar Bhowmik","orcid":"https://orcid.org/0000-0003-1599-5082"},"institutions":[{"id":"https://openalex.org/I205746353","display_name":"University of Dhaka","ror":"https://ror.org/05wv2vq37","country_code":"BD","type":"education","lineage":["https://openalex.org/I205746353"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Samir K. Bhowmik","raw_affiliation_strings":["University of Dhaka","Department of Mathematics, University of Dhaka, 1000 Dhaka, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Dhaka","institution_ids":["https://openalex.org/I205746353"]},{"raw_affiliation_string":"Department of Mathematics, University of Dhaka, 1000 Dhaka, Bangladesh","institution_ids":["https://openalex.org/I205746353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040768839","display_name":"K. R. Raslan","orcid":"https://orcid.org/0000-0001-7631-4071"},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]},{"id":"https://openalex.org/I4210125886","display_name":"Al-Azhar University","ror":"https://ror.org/03ewepe58","country_code":"ID","type":"education","lineage":["https://openalex.org/I4210125886"]}],"countries":["EG","ID"],"is_corresponding":false,"raw_author_name":"Kamal R. Raslan","raw_affiliation_strings":["Al-Azhar University","Department of Mathematics, Al-Azhar University, Nasr-City, Cairo, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Al-Azhar University","institution_ids":["https://openalex.org/I4210125886"]},{"raw_affiliation_string":"Department of Mathematics, Al-Azhar University, Nasr-City, Cairo, Egypt","institution_ids":["https://openalex.org/I184834183"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5012,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.81558081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"3","first_page":"373","last_page":"388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9818999767303467,"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/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.8509732484817505},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6612197160720825},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6446713209152222},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6293800473213196},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5401687622070312},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5017836093902588},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48686519265174866},{"id":"https://openalex.org/keywords/von-neumann-stability-analysis","display_name":"Von Neumann stability analysis","score":0.48485836386680603},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4386656582355499},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4117385745048523},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3372873067855835},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.33322855830192566},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15723451972007751},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1506398618221283},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10826778411865234},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09691327810287476}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.8509732484817505},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6612197160720825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6446713209152222},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6293800473213196},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5401687622070312},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5017836093902588},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48686519265174866},{"id":"https://openalex.org/C71477052","wikidata":"https://www.wikidata.org/wiki/Q458556","display_name":"Von Neumann stability analysis","level":4,"score":0.48485836386680603},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4386656582355499},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4117385745048523},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3372873067855835},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.33322855830192566},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15723451972007751},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1506398618221283},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10826778411865234},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09691327810287476},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3846/13926292.2017.1313329","is_oa":true,"landing_page_url":"https://doi.org/10.3846/13926292.2017.1313329","pdf_url":"https://journals.vgtu.lt/index.php/MMA/article/download/902/682","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:45fc0402fb1148e1b5e8d255f864b950","is_oa":false,"landing_page_url":"https://doaj.org/article/45fc0402fb1148e1b5e8d255f864b950","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"Mathematical Modelling and Analysis, Vol 22, Iss 3 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3846/13926292.2017.1313329","is_oa":true,"landing_page_url":"https://doi.org/10.3846/13926292.2017.1313329","pdf_url":"https://journals.vgtu.lt/index.php/MMA/article/download/902/682","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2614366477.pdf","grobid_xml":"https://content.openalex.org/works/W2614366477.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W280536263","https://openalex.org/W821150639","https://openalex.org/W1555557982","https://openalex.org/W1964123610","https://openalex.org/W1979722387","https://openalex.org/W1995329412","https://openalex.org/W2008322089","https://openalex.org/W2042642553","https://openalex.org/W2043014870","https://openalex.org/W2065015198","https://openalex.org/W2081663242","https://openalex.org/W2082621526","https://openalex.org/W2083488075","https://openalex.org/W2086662352","https://openalex.org/W2118301262","https://openalex.org/W2137975300","https://openalex.org/W2144899139","https://openalex.org/W2147860878","https://openalex.org/W2157763285","https://openalex.org/W2184710225","https://openalex.org/W2275336155","https://openalex.org/W2529310650","https://openalex.org/W2567233933","https://openalex.org/W2619615431","https://openalex.org/W2741641544","https://openalex.org/W3148263248","https://openalex.org/W4246113444","https://openalex.org/W4388020118"],"related_works":["https://openalex.org/W2078318892","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W2169469906","https://openalex.org/W322101810","https://openalex.org/W2384941625","https://openalex.org/W2131278000","https://openalex.org/W2889856026","https://openalex.org/W2009058751","https://openalex.org/W2478942264"],"abstract_inverted_index":{"In":[0],"the":[1,10,31,50,69,72,75,79,96],"present":[2],"paper,":[3],"a":[4],"numerical":[5,11],"method":[6,25,36],"is":[7,37,85,100],"proposed":[8],"for":[9],"solution":[12],"of":[13,49,59,71,74,83,105],"Rosenau-KdV":[14],"equation":[15],"with":[16,26],"appropriate":[17],"initial":[18,90],"and":[19,54,61],"boundary":[20],"conditions":[21],"by":[22,87],"using":[23,43],"collocation":[24],"septic":[27],"B-spline":[28],"functions":[29],"on":[30],"uniform":[32],"mesh":[33],"points.":[34],"The":[35],"shown":[38],"to":[39,67,102],"be":[40],"unconditionally":[41],"stable":[42],"von-Neumann":[44],"technique.":[45],"To":[46],"check":[47],"accuracy":[48],"error":[51],"norms":[52],"L2":[53],"L\u221e":[55],"are":[56,65],"computed.":[57],"Interaction":[58],"two":[60],"three":[62],"solitary":[63,76],"waves":[64,77],"used":[66],"discuss":[68],"effect":[70],"behavior":[73],"during":[78],"interaction.":[80],"Furthermore,":[81],"evolution":[82],"solitons":[84],"illustrated":[86],"undular":[88],"bore":[89],"condition.":[91],"These":[92],"results":[93],"show":[94],"that":[95],"technique":[97],"introduced":[98],"here":[99],"suitable":[101],"investigate":[103],"behaviors":[104],"shallow":[106],"water":[107],"waves.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
