{"id":"https://openalex.org/W2154843942","doi":"https://doi.org/10.1109/icmlc.2011.6016817","title":"Homotopy perturbation method based on Green function for solving non-linear singular boundary value problems","display_name":"Homotopy perturbation method based on Green function for solving non-linear singular boundary value problems","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2154843942","doi":"https://doi.org/10.1109/icmlc.2011.6016817","mag":"2154843942"},"language":"en","primary_location":{"id":"doi:10.1109/icmlc.2011.6016817","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icmlc.2011.6016817","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 International Conference on Machine Learning and Cybernetics","raw_type":"proceedings-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/A5013318460","display_name":"Xufeng Shang","orcid":null},"institutions":[{"id":"https://openalex.org/I55538621","display_name":"China Jiliang University","ror":"https://ror.org/05v1y0t93","country_code":"CN","type":"education","lineage":["https://openalex.org/I55538621"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xufeng Shang","raw_affiliation_strings":["Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou, Zhejiang, China"],"affiliations":[{"raw_affiliation_string":"Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou, Zhejiang, China","institution_ids":["https://openalex.org/I55538621"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046428374","display_name":"Yubo Yuan","orcid":"https://orcid.org/0000-0002-7577-3257"},"institutions":[{"id":"https://openalex.org/I55538621","display_name":"China Jiliang University","ror":"https://ror.org/05v1y0t93","country_code":"CN","type":"education","lineage":["https://openalex.org/I55538621"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yubo Yuan","raw_affiliation_strings":["Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou, Zhejiang, China"],"affiliations":[{"raw_affiliation_string":"Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou, Zhejiang, China","institution_ids":["https://openalex.org/I55538621"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013318460"],"corresponding_institution_ids":["https://openalex.org/I55538621"],"apc_list":null,"apc_paid":null,"fwci":0.229,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.56909789,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"851","last_page":"855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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":0.9947999715805054,"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":0.9943000078201294,"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/singularity","display_name":"Singularity","score":0.7285597324371338},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.7261700630187988},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6401073932647705},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6151002645492554},{"id":"https://openalex.org/keywords/homotopy-perturbation-method","display_name":"Homotopy perturbation method","score":0.5950748324394226},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4923287630081177},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.48447203636169434},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.468142569065094},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.4454011619091034},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11587491631507874}],"concepts":[{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7285597324371338},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.7261700630187988},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6401073932647705},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6151002645492554},{"id":"https://openalex.org/C91328119","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy perturbation method","level":3,"score":0.5950748324394226},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4923287630081177},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.48447203636169434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.468142569065094},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.4454011619091034},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11587491631507874}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icmlc.2011.6016817","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icmlc.2011.6016817","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 International Conference on Machine Learning and Cybernetics","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1977400321","https://openalex.org/W1996986887","https://openalex.org/W2003806194","https://openalex.org/W2014921298","https://openalex.org/W2015256935","https://openalex.org/W2044299439","https://openalex.org/W2071671741","https://openalex.org/W2075201176","https://openalex.org/W2085931380","https://openalex.org/W2103238585","https://openalex.org/W2114502388"],"related_works":["https://openalex.org/W2088506180","https://openalex.org/W2362256999","https://openalex.org/W2188605998","https://openalex.org/W2087729225","https://openalex.org/W1964997874","https://openalex.org/W1545358442","https://openalex.org/W4239956528","https://openalex.org/W1497843313","https://openalex.org/W2127579732","https://openalex.org/W2151283633"],"abstract_inverted_index":{"Non-linear":[0],"singular":[1],"two-point":[2],"boundary":[3],"value":[4],"problems":[5,52],"arise":[6],"in":[7,67],"many":[8],"branches":[9],"of":[10,34,75,82],"applied":[11],"mathematics":[12],"and":[13,55,65],"physics":[14],"such":[15],"as":[16],"gas":[17],"dynamics,":[18],"biology":[19],"science,":[20],"etc.":[21],"In":[22],"this":[23,35,83],"paper,":[24],"we":[25],"present":[26,88],"a":[27,32,89],"high-accurate":[28],"method":[29,61,84],"to":[30,87,92],"solve":[31],"class":[33],"type":[36],"equations":[37,69],"by":[38],"using":[39],"Homotopy":[40],"perturbation":[41],"method(HPM)":[42],"based":[43],"on":[44],"Green":[45],"function.":[46],"Some":[47],"examples":[48],"from":[49],"physical":[50],"model":[51],"are":[53],"given":[54],"the":[56,60,73,76,94,98],"results":[57],"reveal":[58],"that":[59],"is":[62,78,85],"very":[63],"effective":[64],"convenient":[66],"solving":[68],"with":[70],"singularity,":[71],"where":[72],"convergence":[74],"result":[77],"observed.":[79],"The":[80],"advantage":[81],"employed":[86],"reliable":[90],"framework":[91],"overcome":[93],"singularity":[95],"behavior":[96],"at":[97],"point":[99],"x":[100],"=":[101],"0":[102],"for":[103],"all":[104],"models.":[105]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
