{"id":"https://openalex.org/W4396809352","doi":"https://doi.org/10.1007/s12190-024-02098-0","title":"A numerical technique based on Legendre wavelet for linear and nonlinear hyperbolic telegraph equation","display_name":"A numerical technique based on Legendre wavelet for linear and nonlinear hyperbolic telegraph equation","publication_year":2024,"publication_date":"2024-05-10","ids":{"openalex":"https://openalex.org/W4396809352","doi":"https://doi.org/10.1007/s12190-024-02098-0"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-024-02098-0","doi":"https://doi.org/10.1007/s12190-024-02098-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-024-02098-0","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5101604385","display_name":"Basharat Hussain","orcid":"https://orcid.org/0000-0003-3615-4370","observed_orcids":["https://orcid.org/0000-0003-3615-4370"]},"institutions":[{"id":"https://openalex.org/I3133391162","display_name":"Maulana Azad National Urdu University","ror":"https://ror.org/020an1644","country_code":"IN","type":"education","lineage":["https://openalex.org/I3133391162"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Basharat Hussain","raw_affiliation_strings":["Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, Telangana, 500032, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, Telangana, 500032, India","institution_ids":["https://openalex.org/I3133391162"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090337506","display_name":"Mo Faheem","orcid":"https://orcid.org/0000-0002-6595-8485","observed_orcids":["https://orcid.org/0000-0002-6595-8485"]},"institutions":[{"id":"https://openalex.org/I4210153924","display_name":"National Institute of Technology Andhra Pradesh","ror":"https://ror.org/0456pcg54","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210153924"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mo Faheem","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Andhra Pradesh, Tadepalligudem, Andhra Pradesh, 534101, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Andhra Pradesh, Tadepalligudem, Andhra Pradesh, 534101, India","institution_ids":["https://openalex.org/I4210153924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086964029","display_name":"Arshad Hussain Khan","orcid":"https://orcid.org/0000-0003-3783-188X","observed_orcids":["https://orcid.org/0000-0003-3783-188X"]},"institutions":[{"id":"https://openalex.org/I59475050","display_name":"Jamia Millia Islamia","ror":"https://ror.org/00pnhhv55","country_code":"IN","type":"education","lineage":["https://openalex.org/I59475050"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Arshad Khan","raw_affiliation_strings":["Department of Mathematics, Jamia Millia Islamia, New Delhi, Delhi, 110025, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jamia Millia Islamia, New Delhi, Delhi, 110025, India","institution_ids":["https://openalex.org/I59475050"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086964029"],"corresponding_institution_ids":["https://openalex.org/I59475050"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":3.4318,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.93919683,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"70","issue":"4","first_page":"3661","last_page":"3684"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.4147999882698059,"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 Solvers for Ordinary Differential Equations","score":0.4147999882698059,"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":0.30660000443458557,"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":0.06970000267028809,"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/hyperbolic-telegraph-equation","display_name":"hyperbolic telegraph equation","score":0.9330000281333923},{"id":"https://openalex.org/keywords/legendre-wavelets","display_name":"Legendre wavelets","score":0.7799999713897705},{"id":"https://openalex.org/keywords/wavelet-collocation-method","display_name":"wavelet collocation method","score":0.9900000095367432},{"id":"https://openalex.org/keywords/nonlinear-partial-differential-equations","display_name":"nonlinear partial differential equations","score":0.875},{"id":"https://openalex.org/keywords/linear-partial-differential-equations","display_name":"linear partial differential equations","score":0.800000011920929},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.7580000162124634}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.6655383706092834},{"id":"https://openalex.org/C124566792","wikidata":"https://www.wikidata.org/wiki/Q1156880","display_name":"Telegrapher's equations","level":3,"score":0.6047249436378479},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.5961847305297852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5880535244941711},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5807101726531982},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5309063196182251},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.5275623202323914},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5158550143241882},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48055651783943176},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.4606608748435974},{"id":"https://openalex.org/C36956377","wikidata":"https://www.wikidata.org/wiki/Q228376","display_name":"Associated Legendre polynomials","level":5,"score":0.44503557682037354},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.22957384586334229},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21783447265625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16931435465812683},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.16519084572792053},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.10170239210128784},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.09438076615333557},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0812438428401947},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C33441834","wikidata":"https://www.wikidata.org/wiki/Q693004","display_name":"Transmission line","level":2,"score":0.0},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12190-024-02098-0","doi":"https://doi.org/10.1007/s12190-024-02098-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-024-02098-0","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1772313798","https://openalex.org/W1965923710","https://openalex.org/W1973769870","https://openalex.org/W2000548100","https://openalex.org/W2000593908","https://openalex.org/W2002415091","https://openalex.org/W2004176627","https://openalex.org/W2006719818","https://openalex.org/W2030662238","https://openalex.org/W2036594442","https://openalex.org/W2040466254","https://openalex.org/W2040471701","https://openalex.org/W2044062963","https://openalex.org/W2052493381","https://openalex.org/W2053304140","https://openalex.org/W2070594358","https://openalex.org/W2083225982","https://openalex.org/W2088680311","https://openalex.org/W2094585768","https://openalex.org/W2096261291","https://openalex.org/W2128849091","https://openalex.org/W2130254387","https://openalex.org/W2137236532","https://openalex.org/W2142524161","https://openalex.org/W2149946807","https://openalex.org/W2163055192","https://openalex.org/W2188420717","https://openalex.org/W2468447016","https://openalex.org/W2507264573","https://openalex.org/W2609268354","https://openalex.org/W2801119887","https://openalex.org/W2940510923","https://openalex.org/W3015192910","https://openalex.org/W3020017829","https://openalex.org/W3047072983","https://openalex.org/W3080444122","https://openalex.org/W3090694125","https://openalex.org/W3124319204","https://openalex.org/W3170317109","https://openalex.org/W3172981583","https://openalex.org/W4231998994","https://openalex.org/W4239345809","https://openalex.org/W4308599805","https://openalex.org/W4309748743"],"related_works":["https://openalex.org/W3047072983","https://openalex.org/W3121759679","https://openalex.org/W4251766215","https://openalex.org/W1988523854","https://openalex.org/W4390780502","https://openalex.org/W2794040592","https://openalex.org/W2767121668","https://openalex.org/W7166061201","https://openalex.org/W4415096113","https://openalex.org/W2735727199"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2024-05-11T00:00:00"}