{"id":"https://openalex.org/W1970582848","doi":"https://doi.org/10.1080/00207160410001660817","title":"Collocation solution of the Korteweg\u2013de Vries equation using septic splines","display_name":"Collocation solution of the Korteweg\u2013de Vries equation using septic splines","publication_year":2004,"publication_date":"2004-03-01","ids":{"openalex":"https://openalex.org/W1970582848","doi":"https://doi.org/10.1080/00207160410001660817","mag":"1970582848"},"language":"en","primary_location":{"id":"doi:10.1080/00207160410001660817","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160410001660817","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/A5101642042","display_name":"A.A. Soliman","orcid":"https://orcid.org/0000-0002-8792-7567"},"institutions":[{"id":"https://openalex.org/I1325784139","display_name":"Yahoo (United Kingdom)","ror":"https://ror.org/038p3gq39","country_code":"GB","type":"company","lineage":["https://openalex.org/I1325784139","https://openalex.org/I4210134091"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"A. A. Soliman","raw_affiliation_strings":["Correspondenceasoliman_99@yahoo.com"],"affiliations":[{"raw_affiliation_string":"Correspondenceasoliman_99@yahoo.com","institution_ids":["https://openalex.org/I1325784139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101642042"],"corresponding_institution_ids":["https://openalex.org/I1325784139"],"apc_list":null,"apc_paid":null,"fwci":1.4829,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.80869716,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"81","issue":"3","first_page":"325","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9976000189781189,"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":0.9976000189781189,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7036200761795044},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.6985901594161987},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5397196412086487},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44468677043914795},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.4144403040409088},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3642394542694092},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.15787312388420105},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.1485181450843811},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10986343026161194},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09833335876464844}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7036200761795044},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.6985901594161987},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5397196412086487},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44468677043914795},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.4144403040409088},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3642394542694092},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.15787312388420105},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.1485181450843811},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10986343026161194},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09833335876464844},{"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/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160410001660817","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160410001660817","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1968287683","https://openalex.org/W1974838542","https://openalex.org/W2025712879","https://openalex.org/W2044891421","https://openalex.org/W2047974047","https://openalex.org/W2050639649","https://openalex.org/W2055623556","https://openalex.org/W2079285567","https://openalex.org/W2999792156"],"related_works":["https://openalex.org/W2078318892","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W322101810","https://openalex.org/W2384941625","https://openalex.org/W2889856026","https://openalex.org/W2009058751","https://openalex.org/W1989122168","https://openalex.org/W2131278000","https://openalex.org/W2953063785"],"abstract_inverted_index":{"Abstract":[0],"Numerical":[1],"solutions":[2],"for":[3],"the":[4,10,28,31,41,51],"Korteweg\u2013de":[5],"Vries":[6],"equation":[7],"based":[8],"on":[9],"collocation":[11],"method":[12,32],"using":[13],"septic":[14],"splines":[15],"as":[16],"element":[17],"shape":[18],"functions":[19],"are":[20],"set":[21],"up.":[22],"A":[23,37],"linear":[24],"stability":[25],"analysis":[26],"of":[27,45],"scheme":[29,55],"shows":[30],"to":[33,49,64],"be":[34,65],"unconditionally":[35],"stable.":[36],"test":[38],"problem":[39],"concerning":[40],"development":[42],"and":[43,62,67],"motion":[44],"solitons":[46],"is":[47,56],"used":[48],"validate":[50],"method.":[52],"The":[53],"numerical":[54],"compared":[57],"with":[58],"other":[59],"published":[60],"methods":[61],"shown":[63],"accurate":[66],"efficient.":[68],"Keywords:":[69],"KdV":[70],"equationSeptic":[71],"splineCollocation":[72],"solution":[73]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
