{"id":"https://openalex.org/W2077249909","doi":"https://doi.org/10.1016/s0096-3003(97)10126-6","title":"Efficient shooting algorithms for solving the nonlinear one-dimensional scalar Helmholtz equation","display_name":"Efficient shooting algorithms for solving the nonlinear one-dimensional scalar Helmholtz equation","publication_year":1998,"publication_date":"1998-09-01","ids":{"openalex":"https://openalex.org/W2077249909","doi":"https://doi.org/10.1016/s0096-3003(97)10126-6","mag":"2077249909"},"language":"en","primary_location":{"id":"doi:10.1016/s0096-3003(97)10126-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(97)10126-6","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/A5101570289","display_name":"Salvador Jim\u00e9nez","orcid":"https://orcid.org/0000-0001-5265-7360"},"institutions":[{"id":"https://openalex.org/I4210147442","display_name":"Universidad Alfonso X el Sabio","ror":"https://ror.org/054ewwr15","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210147442"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"S Jim\u00e9nez","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Universidad Alfonso X El Sabio, Avenida de la Universidad 1, E-28 691 Villanueva de la Ca\u00f1ada, Madrid, Spain","Departamento de Matem\u00e1tica Aplicada, Universidad Alfonso X El Sabio, Avenida de la Universidad 1, E-28 691 Villanueva de la Ca\u00f1ada, Madrid, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Universidad Alfonso X El Sabio, Avenida de la Universidad 1, E-28 691 Villanueva de la Ca\u00f1ada, Madrid, Spain","institution_ids":["https://openalex.org/I4210147442"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Universidad Alfonso X El Sabio, Avenida de la Universidad 1, E-28 691 Villanueva de la Ca\u00f1ada, Madrid, Spain#TAB#","institution_ids":["https://openalex.org/I4210147442"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108415826","display_name":"S. A. Bulgakov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210118429","display_name":"Instituto de Ciencia de Materiales de Madrid","ror":"https://ror.org/02qqy8j09","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210118429"]},{"id":"https://openalex.org/I134820265","display_name":"Consejo Superior de Investigaciones Cient\u00edficas","ror":"https://ror.org/02gfc7t72","country_code":"ES","type":"funder","lineage":["https://openalex.org/I134820265"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S Bulgakov","raw_affiliation_strings":["Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cient\u0131\u0301ficas, Cantoblanco, E-28 049 Madrid, Spain","Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cient\u0131ficas, Cantoblanco, E-28 049 Madrid, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cient\u0131\u0301ficas, Cantoblanco, E-28 049 Madrid, Spain","institution_ids":["https://openalex.org/I4210118429","https://openalex.org/I134820265"]},{"raw_affiliation_string":"Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cient\u0131ficas, Cantoblanco, E-28 049 Madrid, Spain#TAB#","institution_ids":["https://openalex.org/I134820265"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065856237","display_name":"Luis V\u00e1zquez","orcid":"https://orcid.org/0000-0003-4054-1197"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"L V\u00e1zquez","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Escuela Superior de Inform\u00e1tica, Universidad Complutense, E-28040 Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Escuela Superior de Inform\u00e1tica, Universidad Complutense, E-28040 Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101570289"],"corresponding_institution_ids":["https://openalex.org/I4210147442"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.5287,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69129513,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"2-3","first_page":"101","last_page":"114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10299","display_name":"Photonic and Optical Devices","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10299","display_name":"Photonic and Optical Devices","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11050","display_name":"Photorefractive and Nonlinear Optics","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11723","display_name":"Optical Coatings and Gratings","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.7039536833763123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.61026930809021},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5690973997116089},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5497964024543762},{"id":"https://openalex.org/keywords/scalar-field","display_name":"Scalar field","score":0.5111389756202698},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48011231422424316},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.47914451360702515},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4599844813346863},{"id":"https://openalex.org/keywords/shooting-method","display_name":"Shooting method","score":0.4589570164680481},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42769503593444824},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3526749610900879},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13636142015457153},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0994320809841156}],"concepts":[{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7039536833763123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.61026930809021},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5690973997116089},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5497964024543762},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.5111389756202698},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48011231422424316},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.47914451360702515},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4599844813346863},{"id":"https://openalex.org/C4195266","wikidata":"https://www.wikidata.org/wiki/Q1749769","display_name":"Shooting method","level":3,"score":0.4589570164680481},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42769503593444824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3526749610900879},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13636142015457153},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0994320809841156},{"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0096-3003(97)10126-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(97)10126-6","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2006812131","https://openalex.org/W2043372944","https://openalex.org/W2052045393","https://openalex.org/W3004157836"],"related_works":["https://openalex.org/W2052131453","https://openalex.org/W2035230787","https://openalex.org/W1992244398","https://openalex.org/W2057106870","https://openalex.org/W2467955472","https://openalex.org/W2103102878","https://openalex.org/W2957740688","https://openalex.org/W2904982713","https://openalex.org/W1992050547","https://openalex.org/W2167106674"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
