{"id":"https://openalex.org/W2073384823","doi":"https://doi.org/10.1016/j.camwa.2011.04.029","title":"A novel method for nonlinear singular fourth order four-point boundary value problems","display_name":"A novel method for nonlinear singular fourth order four-point boundary value problems","publication_year":2011,"publication_date":"2011-05-21","ids":{"openalex":"https://openalex.org/W2073384823","doi":"https://doi.org/10.1016/j.camwa.2011.04.029","mag":"2073384823"},"language":"en","primary_location":{"id":"doi:10.1016/j.camwa.2011.04.029","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2011.04.029","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"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":"Computers &amp; Mathematics with Applications","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/A5037582926","display_name":"Xiuying Li","orcid":"https://orcid.org/0000-0002-7025-6306"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"X.Y. Li","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, PR China","Department of Mathematics, Harbin Institute of Technology, Harbin, HeiLongJiang, 150001, PR China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, PR China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, HeiLongJiang, 150001, PR China#TAB#","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101820488","display_name":"Boying Wu","orcid":"https://orcid.org/0000-0003-3985-3783"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"B.Y. Wu","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, PR China","Department of Mathematics, Harbin Institute of Technology, Harbin, HeiLongJiang, 150001, PR China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, PR China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, HeiLongJiang, 150001, PR China#TAB#","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037582926"],"corresponding_institution_ids":["https://openalex.org/I204983213","https://openalex.org/I4210161462"],"apc_list":{"value":3480,"currency":"USD","value_usd":3480},"apc_paid":null,"fwci":1.2002,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.77722096,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"62","issue":"1","first_page":"27","last_page":"31"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9966999888420105,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9894999861717224,"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/mathematics","display_name":"Mathematics","score":0.8551863431930542},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.6323575377464294},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6283871531486511},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.605446457862854},{"id":"https://openalex.org/keywords/homotopy-perturbation-method","display_name":"Homotopy perturbation method","score":0.5635747909545898},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5158083438873291},{"id":"https://openalex.org/keywords/multi-point","display_name":"Multi point","score":0.4912952780723572},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4906236231327057},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.48756927251815796},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.479245662689209},{"id":"https://openalex.org/keywords/singular-solution","display_name":"Singular solution","score":0.474263072013855},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.46407297253608704},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4601375162601471},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.45963814854621887},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.41806408762931824},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.11347931623458862},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1033163070678711},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07942822575569153},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.07379114627838135}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8551863431930542},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.6323575377464294},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6283871531486511},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.605446457862854},{"id":"https://openalex.org/C91328119","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy perturbation method","level":3,"score":0.5635747909545898},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5158083438873291},{"id":"https://openalex.org/C3020050198","wikidata":"https://www.wikidata.org/wiki/Q6935027","display_name":"Multi point","level":2,"score":0.4912952780723572},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4906236231327057},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.48756927251815796},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.479245662689209},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.474263072013855},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.46407297253608704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4601375162601471},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.45963814854621887},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.41806408762931824},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.11347931623458862},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1033163070678711},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07942822575569153},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.07379114627838135},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":1,"locations":[{"id":"doi:10.1016/j.camwa.2011.04.029","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2011.04.029","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"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":"Computers &amp; Mathematics with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8498585255","display_name":null,"funder_award_id":"11026200","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1527525543","https://openalex.org/W1636478690","https://openalex.org/W1970467391","https://openalex.org/W1978981090","https://openalex.org/W1983714033","https://openalex.org/W1985625439","https://openalex.org/W1989630696","https://openalex.org/W1999776604","https://openalex.org/W2002138473","https://openalex.org/W2003806194","https://openalex.org/W2009343239","https://openalex.org/W2011910223","https://openalex.org/W2019715862","https://openalex.org/W2021155240","https://openalex.org/W2024135740","https://openalex.org/W2024490257","https://openalex.org/W2034471806","https://openalex.org/W2036656081","https://openalex.org/W2041403118","https://openalex.org/W2051661016","https://openalex.org/W2056211983","https://openalex.org/W2057294962","https://openalex.org/W2067238867","https://openalex.org/W2067652448","https://openalex.org/W2068438731","https://openalex.org/W2071432503","https://openalex.org/W2072481813","https://openalex.org/W2074246881","https://openalex.org/W2087226000","https://openalex.org/W2100240867","https://openalex.org/W2106912849","https://openalex.org/W2107837511","https://openalex.org/W2108059751","https://openalex.org/W2127579732","https://openalex.org/W2137653426","https://openalex.org/W2165917005","https://openalex.org/W2262068877","https://openalex.org/W2272349946","https://openalex.org/W2313043415","https://openalex.org/W2319727456","https://openalex.org/W2322549732","https://openalex.org/W2324468482","https://openalex.org/W3005644401","https://openalex.org/W6694088662"],"related_works":["https://openalex.org/W2088506180","https://openalex.org/W2188605998","https://openalex.org/W2087729225","https://openalex.org/W1545358442","https://openalex.org/W4239956528","https://openalex.org/W2040041204","https://openalex.org/W2515699486","https://openalex.org/W1497843313","https://openalex.org/W2127579732","https://openalex.org/W2974754464"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
