{"id":"https://openalex.org/W2034832920","doi":"https://doi.org/10.1016/s0096-3003(03)00305-9","title":"Comparing numerical methods for Helmholtz equation model problem","display_name":"Comparing numerical methods for Helmholtz equation model problem","publication_year":2003,"publication_date":"2003-05-12","ids":{"openalex":"https://openalex.org/W2034832920","doi":"https://doi.org/10.1016/s0096-3003(03)00305-9","mag":"2034832920"},"language":"en","primary_location":{"id":"doi:10.1016/s0096-3003(03)00305-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(03)00305-9","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"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":"Applied Mathematics and Computation","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/A5069850068","display_name":"Salah M. El\u2010Sayed","orcid":"https://orcid.org/0000-0001-9885-313X"},"institutions":[{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Salah M. El-Sayed","raw_affiliation_strings":["Department of Mathematics, Benha University, Benha 13518, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Benha University, Benha 13518, Egypt","institution_ids":["https://openalex.org/I207547235"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102024977","display_name":"Do\u01e7an Kaya","orcid":"https://orcid.org/0000-0003-4773-1313"},"institutions":[{"id":"https://openalex.org/I143396566","display_name":"F\u0131rat University","ror":"https://ror.org/05teb7b63","country_code":"TR","type":"education","lineage":["https://openalex.org/I143396566"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Do\u01e7an Kaya","raw_affiliation_strings":["Department of Mathematics, Firat University, Elazig 23119, Turkey","Department of Mathematics , Firat University , Elazig, 23119, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Firat University, Elazig 23119, Turkey","institution_ids":["https://openalex.org/I143396566"]},{"raw_affiliation_string":"Department of Mathematics , Firat University , Elazig, 23119, Turkey","institution_ids":["https://openalex.org/I143396566"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069850068"],"corresponding_institution_ids":["https://openalex.org/I207547235"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":4.4762,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.94475418,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"150","issue":"3","first_page":"763","last_page":"773"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"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":0.9997000098228455,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9944000244140625,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/adomian-decomposition-method","display_name":"Adomian decomposition method","score":0.8135156631469727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7230396866798401},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.6638762354850769},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.621311604976654},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6112450957298279},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5774602293968201},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.5441958904266357},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.5433858036994934},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.5378981828689575},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5086454153060913},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4964926838874817},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.4878118336200714},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.44005870819091797},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4387955367565155},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3419375717639923},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18469151854515076},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.10705140233039856}],"concepts":[{"id":"https://openalex.org/C120317633","wikidata":"https://www.wikidata.org/wiki/Q3042796","display_name":"Adomian decomposition method","level":3,"score":0.8135156631469727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7230396866798401},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.6638762354850769},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.621311604976654},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6112450957298279},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5774602293968201},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.5441958904266357},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.5433858036994934},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.5378981828689575},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5086454153060913},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4964926838874817},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.4878118336200714},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.44005870819091797},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4387955367565155},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3419375717639923},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18469151854515076},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.10705140233039856},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0096-3003(03)00305-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(03)00305-9","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"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":"Applied Mathematics and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311015","display_name":"Firat \u00dcniversitesi","ror":"https://ror.org/05teb7b63"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1518833317","https://openalex.org/W1558933379","https://openalex.org/W1560556759","https://openalex.org/W1580458380","https://openalex.org/W1966171107","https://openalex.org/W1967339834","https://openalex.org/W1967822199","https://openalex.org/W1975341570","https://openalex.org/W1978021078","https://openalex.org/W1986824988","https://openalex.org/W1988862753","https://openalex.org/W1995365180","https://openalex.org/W1997290136","https://openalex.org/W2012098823","https://openalex.org/W2020773907","https://openalex.org/W2029933550","https://openalex.org/W2035064076","https://openalex.org/W2049446621","https://openalex.org/W2056045774","https://openalex.org/W2061429546","https://openalex.org/W2068264104","https://openalex.org/W2089399146","https://openalex.org/W2122123126","https://openalex.org/W2141673032","https://openalex.org/W2898916015","https://openalex.org/W4249517526","https://openalex.org/W6673159411"],"related_works":["https://openalex.org/W4365420316","https://openalex.org/W2089904505","https://openalex.org/W2184238946","https://openalex.org/W2089018597","https://openalex.org/W3176862315","https://openalex.org/W1838417290","https://openalex.org/W1977939012","https://openalex.org/W811173482","https://openalex.org/W2028789925","https://openalex.org/W2373977562"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}