{"id":"https://openalex.org/W2914305944","doi":"https://doi.org/10.1515/cmam-2018-0107","title":"On the Stable Difference Schemes for the Schr\u00f6dinger Equation with Time Delay","display_name":"On the Stable Difference Schemes for the Schr\u00f6dinger Equation with Time Delay","publication_year":2019,"publication_date":"2019-02-15","ids":{"openalex":"https://openalex.org/W2914305944","doi":"https://doi.org/10.1515/cmam-2018-0107","mag":"2914305944"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0107","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0107","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5018925282","display_name":"Allaberen Ashyralyev","orcid":"https://orcid.org/0000-0002-4153-6624"},"institutions":[{"id":"https://openalex.org/I69050122","display_name":"Near East University","ror":"https://ror.org/02x8svs93","country_code":"CY","type":"education","lineage":["https://openalex.org/I69050122"]},{"id":"https://openalex.org/I4210151480","display_name":"Institute of Mathematics and Mathematical Modeling","ror":"https://ror.org/05xx3wf87","country_code":"KZ","type":"government","lineage":["https://openalex.org/I4210151480"]},{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]},{"id":"https://openalex.org/I51780484","display_name":"Mersin \u00dcniversitesi","ror":"https://ror.org/04nqdwb39","country_code":"TR","type":"education","lineage":["https://openalex.org/I51780484"]}],"countries":["CY","KZ","RU","TR"],"is_corresponding":false,"raw_author_name":"Allaberen Ashyralyev","raw_affiliation_strings":["Department of Mathematics , Near East University , Mersin 10 , Turkey ; and Peoples Friendship University Russia, Ul Miklukho Maklaya 6, Moscow 117198, Russia; and Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan","Department of Mathematics, Near East University, Mersin 10, Turkey","Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Near East University , Mersin 10 , Turkey ; and Peoples Friendship University Russia, Ul Miklukho Maklaya 6, Moscow 117198, Russia; and Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan","institution_ids":["https://openalex.org/I4210151480","https://openalex.org/I69050122","https://openalex.org/I126527374"]},{"raw_affiliation_string":"Department of Mathematics, Near East University, Mersin 10, Turkey","institution_ids":["https://openalex.org/I69050122","https://openalex.org/I51780484"]},{"raw_affiliation_string":"Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan","institution_ids":["https://openalex.org/I4210151480"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008777878","display_name":"Deniz A\u011f\u0131rseven","orcid":"https://orcid.org/0000-0002-5585-5837"},"institutions":[{"id":"https://openalex.org/I12387023","display_name":"Trakya University","ror":"https://ror.org/00xa0xn82","country_code":"TR","type":"education","lineage":["https://openalex.org/I12387023"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Deniz Agirseven","raw_affiliation_strings":["Department of Mathematics , Trakya University , 22030 Edirne , Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Trakya University , 22030 Edirne , Turkey","institution_ids":["https://openalex.org/I12387023"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008777878"],"corresponding_institution_ids":["https://openalex.org/I12387023"],"apc_list":null,"apc_paid":null,"fwci":1.9472,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84226259,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"20","issue":"1","first_page":"27","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9980000257492065,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9980000257492065,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9977999925613403,"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":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8043457269668579},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6699230670928955},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6282780170440674},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5661705732345581},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5277919173240662},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5085321664810181},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4927082359790802},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4907130002975464},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4815533459186554},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4740345776081085},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43670859932899475},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4142789840698242},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06408849358558655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8043457269668579},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6699230670928955},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6282780170440674},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5661705732345581},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5277919173240662},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5085321664810181},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4927082359790802},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4907130002975464},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4815533459186554},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4740345776081085},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43670859932899475},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4142789840698242},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06408849358558655},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0107","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0107","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321912","display_name":"Ministry of Education and Science of the Russian Federation","ror":"https://ror.org/00ghqgy32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W24979985","https://openalex.org/W599536832","https://openalex.org/W1923962779","https://openalex.org/W1980233447","https://openalex.org/W1989924738","https://openalex.org/W2000119738","https://openalex.org/W2008117223","https://openalex.org/W2009829732","https://openalex.org/W2012189950","https://openalex.org/W2014608347","https://openalex.org/W2016517222","https://openalex.org/W2020048703","https://openalex.org/W2024501352","https://openalex.org/W2034895882","https://openalex.org/W2041757237","https://openalex.org/W2051309064","https://openalex.org/W2054391845","https://openalex.org/W2061514129","https://openalex.org/W2082080832","https://openalex.org/W2083719667","https://openalex.org/W2091325631","https://openalex.org/W2112087002","https://openalex.org/W2135659811","https://openalex.org/W2135900806","https://openalex.org/W2150503337","https://openalex.org/W2172218605","https://openalex.org/W2216999478","https://openalex.org/W2574909440","https://openalex.org/W2793667768","https://openalex.org/W2794771932","https://openalex.org/W2803634166","https://openalex.org/W2883502549","https://openalex.org/W2990924126","https://openalex.org/W3173980525","https://openalex.org/W4285719527","https://openalex.org/W4298874742"],"related_works":["https://openalex.org/W2293044292","https://openalex.org/W2004407847","https://openalex.org/W3202610955","https://openalex.org/W3140545310","https://openalex.org/W2381443067","https://openalex.org/W2117331926","https://openalex.org/W1987269275","https://openalex.org/W4211161164","https://openalex.org/W2378677214","https://openalex.org/W2375474123"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"the":[2,5,15,19,41,59,63],"present":[3],"paper,":[4],"first":[6],"and":[7],"second":[8],"order":[9],"of":[10,18,43,51,55,62],"accuracy":[11],"difference":[12,45,56],"schemes":[13,46,57],"for":[14,23,40,58,68],"approximate":[16,60],"solutions":[17,42,61],"initial":[20,64],"value":[21,66],"problem":[22],"Schr\u00f6dinger":[24,69],"equation":[25,72],"with":[26],"time":[27],"delay":[28],"in":[29],"a":[30],"Hilbert":[31],"space":[32],"are":[33,80],"presented.":[34,81],"The":[35,49],"theorem":[36],"on":[37,53],"stability":[38,54],"estimates":[39],"these":[44],"is":[47,73],"established.":[48],"application":[50],"theorems":[52],"boundary":[65],"problems":[67],"partial":[70],"differential":[71],"provided.":[74],"Additionally,":[75],"some":[76],"illustrative":[77],"numerical":[78],"results":[79]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-18T08:16:58.900851","created_date":"2025-10-10T00:00:00"}
