{"id":"https://openalex.org/W2331069477","doi":"https://doi.org/10.7763/ijapm.2013.v3.190","title":"Legendre Wavelets-Picard Iteration Method for Solution of Nonlinear Initial Value Problems","display_name":"Legendre Wavelets-Picard Iteration Method for Solution of Nonlinear Initial Value Problems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2331069477","doi":"https://doi.org/10.7763/ijapm.2013.v3.190","mag":"2331069477"},"language":"en","primary_location":{"id":"doi:10.7763/ijapm.2013.v3.190","doi":"https://doi.org/10.7763/ijapm.2013.v3.190","is_oa":false,"landing_page_url":"https://doi.org/10.7763/ijapm.2013.v3.190","pdf_url":null,"source":{"id":"https://openalex.org/S2764875742","display_name":"International Journal of Applied Physics and Mathematics","issn_l":"2010-362X","issn":["2010-362X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Physics and Mathematics","raw_type":"journal-article"},"volume":null,"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/A5089866247","display_name":"Fukang Yin","orcid":"https://orcid.org/0000-0002-8353-7000","observed_orcids":["https://orcid.org/0000-0002-8353-7000"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu-Kang Yin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016155785","display_name":"Wang-Yi Han","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang-Yi Han","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101788380","display_name":"Junqiang Song","orcid":"https://orcid.org/0009-0003-2686-566X","observed_orcids":["https://orcid.org/0009-0003-2686-566X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jun-Qiang Song","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110714473","display_name":"Xiaoqun Cao","orcid":"https://orcid.org/0000-0002-6135-0712","observed_orcids":["https://orcid.org/0000-0002-6135-0712"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao-Qun Cao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2451,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.79588745,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"127","last_page":"131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9702000021934509,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9702000021934509,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.006899999920278788,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.005900000222027302,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/legendre-wavelets","display_name":"Legendre wavelets","score":0.9990000128746033},{"id":"https://openalex.org/keywords/picard-iteration","display_name":"Picard iteration","score":0.8769999742507935},{"id":"https://openalex.org/keywords/nonlinear-initial-value-problems","display_name":"nonlinear initial value problems","score":0.9919999837875366},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.7039999961853027},{"id":"https://openalex.org/keywords/dynamical-systems","display_name":"dynamical systems","score":0.4189999997615814}],"concepts":[{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.806943416595459},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.7503114342689514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6880215406417847},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6128698587417603},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6125478148460388},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6054812669754028},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5023250579833984},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43717247247695923},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3261393904685974},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18510791659355164},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.17565873265266418},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14218315482139587},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.11113113164901733},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09660589694976807},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06733852624893188},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.06118118762969971},{"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.7763/ijapm.2013.v3.190","doi":"https://doi.org/10.7763/ijapm.2013.v3.190","is_oa":false,"landing_page_url":"https://doi.org/10.7763/ijapm.2013.v3.190","pdf_url":null,"source":{"id":"https://openalex.org/S2764875742","display_name":"International Journal of Applied Physics and Mathematics","issn_l":"2010-362X","issn":["2010-362X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Physics and Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1975517304","https://openalex.org/W2000852781","https://openalex.org/W2012645543","https://openalex.org/W2025245367","https://openalex.org/W2027115841","https://openalex.org/W2030204179","https://openalex.org/W2030928359","https://openalex.org/W2067548886","https://openalex.org/W2079390764","https://openalex.org/W2094585768","https://openalex.org/W2102907326","https://openalex.org/W2256890785","https://openalex.org/W2562586288","https://openalex.org/W4231998994"],"related_works":["https://openalex.org/W2545227774","https://openalex.org/W3130851271","https://openalex.org/W166303848","https://openalex.org/W2154003217","https://openalex.org/W1563286744","https://openalex.org/W2788092364","https://openalex.org/W2563195118","https://openalex.org/W1643168517","https://openalex.org/W2385225694","https://openalex.org/W2107068834"],"abstract_inverted_index":{"Numerical":[0,74],"methods":[1,71],"for":[2,12,31],"solving":[3,32],"initial":[4],"value":[5],"problems":[6],"(IVPs)":[7],"are":[8],"of":[9,46,58,61],"fundamental":[10],"importance":[11],"analyzing":[13],"and":[14,53,84],"controlling":[15],"dynamic":[16],"systems.":[17],"In":[18],"this":[19],"paper,":[20],"we":[21],"first":[22],"present":[23],"a":[24,59],"new":[25],"Legendre":[26,35],"wavelets-Picard":[27],"iteration":[28,40,51],"method":[29,37,80],"(LWPIM)":[30],"IVPs.":[33],"Combining":[34],"wavelets":[36],"with":[38],"Picard":[39],"method,":[41],"LWPIM":[42],"iteratively":[43],"refines":[44],"estimates":[45],"the":[47,50,56,65,78,91],"solutions":[48],"until":[49],"converges":[52],"can":[54],"avoid":[55],"solution":[57],"system":[60],"algebraic":[62],"equations.":[63],"Furthermore,":[64],"developed":[66],"vector-matrix":[67],"form":[68],"makes":[69],"MCPI":[70],"computationally":[72],"efficient.":[73],"results":[75],"show":[76],"that":[77],"proposed":[79],"is":[81],"mathematically":[82],"simple":[83],"easy":[85],"to":[86],"implement":[87],"while":[88],"still":[89],"keeps":[90],"high":[92],"accuracy.":[93]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}