{"id":"https://openalex.org/W4393336620","doi":"https://doi.org/10.17762/atnaa.v7.i5.326","title":"Anharmonic oscillator via Legendre and Chebyshev pseudo-spectral methods","display_name":"Anharmonic oscillator via Legendre and Chebyshev pseudo-spectral methods","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4393336620","doi":"https://doi.org/10.17762/atnaa.v7.i5.326"},"language":"en","primary_location":{"id":"doi:10.17762/atnaa.v7.i5.326","doi":"https://doi.org/10.17762/atnaa.v7.i5.326","is_oa":true,"landing_page_url":"https://doi.org/10.17762/atnaa.v7.i5.326","pdf_url":"https://atnaea.org/index.php/journal/article/download/326/260","source":{"id":"https://openalex.org/S4210172188","display_name":"Advances in the Theory of Nonlinear Analysis and its Application","issn_l":"2587-2648","issn":["2587-2648"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["poland-20","russia-white-list-2"],"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":"Advances in the Theory of Nonlinear Analysis and its Application","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://atnaea.org/index.php/journal/article/download/326/260","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104267172","display_name":"M Erhan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I76806599","display_name":"Adnan Menderes University","ror":"https://ror.org/03n7yzv56","country_code":"TR","type":"education","lineage":["https://openalex.org/I76806599"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"\u02d9 Inci M. Erhan, Saeida M. Wlie","raw_affiliation_strings":["Department of Computer Engineering, Ayd\u0131n Adnan Menderes University, 09010, Ayd\u0131n, T\u00fcrkiye"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, Ayd\u0131n Adnan Menderes University, 09010, Ayd\u0131n, T\u00fcrkiye","institution_ids":["https://openalex.org/I76806599"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5104267172"],"corresponding_institution_ids":["https://openalex.org/I76806599"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20792289,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.6035000085830688,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.6035000085830688,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.15700000524520874,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.1412000060081482,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/anharmonic-oscillator","display_name":"anharmonic oscillator","score":1.0},{"id":"https://openalex.org/keywords/schrodinger-equation","display_name":"Schr\u00f6dinger equation","score":0.9599999785423279},{"id":"https://openalex.org/keywords/pseudospectral-method","display_name":"pseudospectral method","score":0.8180000185966492},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.9150000214576721},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":1.0},{"id":"https://openalex.org/keywords/similarity-transformation","display_name":"similarity transformation","score":0.9490000009536743},{"id":"https://openalex.org/keywords/symmetric-eigenvalue-problem","display_name":"symmetric eigenvalue problem","score":0.6470000147819519}],"concepts":[{"id":"https://openalex.org/C147724859","wikidata":"https://www.wikidata.org/wiki/Q545228","display_name":"Anharmonicity","level":2,"score":0.7963600754737854},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.7606112360954285},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.7227330803871155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5418511033058167},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4187166392803192},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3999093770980835},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3318207263946533},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.132171630859375}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.17762/atnaa.v7.i5.326","doi":"https://doi.org/10.17762/atnaa.v7.i5.326","is_oa":true,"landing_page_url":"https://doi.org/10.17762/atnaa.v7.i5.326","pdf_url":"https://atnaea.org/index.php/journal/article/download/326/260","source":{"id":"https://openalex.org/S4210172188","display_name":"Advances in the Theory of Nonlinear Analysis and its Application","issn_l":"2587-2648","issn":["2587-2648"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["poland-20","russia-white-list-2"],"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":"Advances in the Theory of Nonlinear Analysis and its Application","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.17762/atnaa.v7.i5.326","doi":"https://doi.org/10.17762/atnaa.v7.i5.326","is_oa":true,"landing_page_url":"https://doi.org/10.17762/atnaa.v7.i5.326","pdf_url":"https://atnaea.org/index.php/journal/article/download/326/260","source":{"id":"https://openalex.org/S4210172188","display_name":"Advances in the Theory of Nonlinear Analysis and its Application","issn_l":"2587-2648","issn":["2587-2648"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["poland-20","russia-white-list-2"],"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":"Advances in the Theory of Nonlinear Analysis and its Application","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393336620.pdf","grobid_xml":"https://content.openalex.org/works/W4393336620.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1971940699","https://openalex.org/W1981027565","https://openalex.org/W1994326771","https://openalex.org/W1995772294","https://openalex.org/W2072653497","https://openalex.org/W2953850379","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W1976011360","https://openalex.org/W2042277087","https://openalex.org/W6989277542","https://openalex.org/W2372953635","https://openalex.org/W2083427104","https://openalex.org/W2064390728","https://openalex.org/W2907631569","https://openalex.org/W4417101010","https://openalex.org/W2302533003","https://openalex.org/W3185990950"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3],"introduce":[4],"the":[5,15,24,44,47,65,76],"pseudospectral":[6],"methods":[7],"based":[8],"on":[9],"Chebyshev":[10],"and":[11,75,79],"Legendre":[12],"polynomials":[13,50],"for":[14],"Schr\u00a8odinger":[16],"equation":[17,67],"of":[18,43,46,68,72],"anharmonic":[19,70],"oscillator.":[20],"The":[21,60],"method":[22,61],"transforms":[23],"problem":[25,31],"into":[26,54],"an":[27,69],"unsym\u0002metric":[28],"matrix":[29,57],"eigenvalue":[30,58],"which":[32],"can":[33],"be":[34],"symmetrized":[35],"by":[36],"using":[37],"a":[38,55],"suitable":[39],"similarity":[40],"transformation.":[41],"Computation":[42],"zeros":[45],"relevant":[48],"orthogonal":[49],"is":[51,62],"also":[52],"converted":[53],"symmetric":[56],"problem.":[59],"applied":[63],"to":[64],"Scr\u00a8odinger":[66],"oscillator":[71],"various":[73],"types":[74],"numerical":[77],"results":[78],"discussed.":[80]},"counts_by_year":[],"updated_date":"2026-09-07T09:17:50.787605","created_date":"2024-03-30T00:00:00"}