{"id":"https://openalex.org/W3000328177","doi":"https://doi.org/10.2478/amcs-2019-0053","title":"A Conservative Scheme with Optimal Error Estimates for a Multidimensional Space\u2013Fractional Gross\u2013Pitaevskii Equation","display_name":"A Conservative Scheme with Optimal Error Estimates for a Multidimensional Space\u2013Fractional Gross\u2013Pitaevskii Equation","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W3000328177","doi":"https://doi.org/10.2478/amcs-2019-0053","mag":"3000328177"},"language":"en","primary_location":{"id":"doi:10.2478/amcs-2019-0053","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2019-0053","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2019-0053","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/amcs-2019-0053","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048088469","display_name":"Ahmed S. Hendy","orcid":"https://orcid.org/0000-0002-3266-7243"},"institutions":[{"id":"https://openalex.org/I130823665","display_name":"Ural Federal University","ror":"https://ror.org/00hs7dr46","country_code":"RU","type":"education","lineage":["https://openalex.org/I130823665"]},{"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","RU"],"is_corresponding":true,"raw_author_name":"Ahmed S. Hendy","raw_affiliation_strings":["Department of Computational Mathematics and Computer Science , Ural Federal University , 19 Mira St., Yekaterinburg 620002 , Russia","Department of Mathematics, Faculty of Science , Benha University , Benha 13511 , Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Computational Mathematics and Computer Science , Ural Federal University , 19 Mira St., Yekaterinburg 620002 , Russia","institution_ids":["https://openalex.org/I130823665"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science , Benha University , Benha 13511 , Egypt","institution_ids":["https://openalex.org/I207547235"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055620640","display_name":"Jorge E. Mac\u00edas\u2010D\u00edaz","orcid":"https://orcid.org/0000-0002-7580-7533"},"institutions":[{"id":"https://openalex.org/I190103667","display_name":"Autonomous University of Aguascalientes","ror":"https://ror.org/03ec8vy26","country_code":"MX","type":"education","lineage":["https://openalex.org/I190103667"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jorge E. Mac\u00edas-D\u00edaz","raw_affiliation_strings":["Department of Mathematics and Physics Autonomous , University of Aguascalientes , Avenida Universidad 940 Ciudad Universitaria, Aguascalientes 20131 , Mexico"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics Autonomous , University of Aguascalientes , Avenida Universidad 940 Ciudad Universitaria, Aguascalientes 20131 , Mexico","institution_ids":["https://openalex.org/I190103667"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048088469"],"corresponding_institution_ids":["https://openalex.org/I130823665","https://openalex.org/I207547235"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":0.3389,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.58761772,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"4","first_page":"713","last_page":"723"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"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":0.9995999932289124,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9973999857902527,"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/mathematics","display_name":"Mathematics","score":0.8097411394119263},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5994702577590942},{"id":"https://openalex.org/keywords/gross\u2013pitaevskii-equation","display_name":"Gross\u2013Pitaevskii equation","score":0.5776454210281372},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5702095627784729},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5487310886383057},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49826979637145996},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.49576839804649353},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4932810664176941},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.46828386187553406},{"id":"https://openalex.org/keywords/angular-momentum","display_name":"Angular momentum","score":0.4265560209751129},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3621433675289154},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.14123007655143738},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09827020764350891},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09109607338905334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0854417085647583}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8097411394119263},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5994702577590942},{"id":"https://openalex.org/C2776902821","wikidata":"https://www.wikidata.org/wiki/Q910667","display_name":"Gross\u2013Pitaevskii equation","level":3,"score":0.5776454210281372},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5702095627784729},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5487310886383057},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49826979637145996},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49576839804649353},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4932810664176941},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.46828386187553406},{"id":"https://openalex.org/C155675718","wikidata":"https://www.wikidata.org/wiki/Q161254","display_name":"Angular momentum","level":2,"score":0.4265560209751129},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3621433675289154},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.14123007655143738},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09827020764350891},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09109607338905334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0854417085647583},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"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},{"id":"https://openalex.org/C37589322","wikidata":"https://www.wikidata.org/wiki/Q46202","display_name":"Bose\u2013Einstein condensate","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2478/amcs-2019-0053","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2019-0053","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2019-0053","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5ccf40ef1f7e4f6db3bcd64a38ffbcc8","is_oa":true,"landing_page_url":"https://doaj.org/article/5ccf40ef1f7e4f6db3bcd64a38ffbcc8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Applied Mathematics and Computer Science, Vol 29, Iss 4, Pp 713-723 (2019)","raw_type":"article"},{"id":"pmh:oai:elar.urfu.ru:10995/90422","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85078192086","pdf_url":null,"source":{"id":"https://openalex.org/S4306401522","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:jah.su:record/340600","is_oa":true,"landing_page_url":"http://hdl.handle.net/10995/90422","pdf_url":null,"source":{"id":"https://openalex.org/S4306401523","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/amcs-2019-0053","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2019-0053","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2019-0053","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1988403100","display_name":null,"funder_award_id":"19-01-00019","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000328177.pdf","grobid_xml":"https://content.openalex.org/works/W3000328177.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W755756226","https://openalex.org/W1974367765","https://openalex.org/W1987668201","https://openalex.org/W1988322580","https://openalex.org/W1996761814","https://openalex.org/W2001011967","https://openalex.org/W2006165875","https://openalex.org/W2019522628","https://openalex.org/W2026106782","https://openalex.org/W2039324033","https://openalex.org/W2056904916","https://openalex.org/W2062701522","https://openalex.org/W2064260985","https://openalex.org/W2065232540","https://openalex.org/W2072306326","https://openalex.org/W2078210968","https://openalex.org/W2093001693","https://openalex.org/W2094706142","https://openalex.org/W2096099997","https://openalex.org/W2129061269","https://openalex.org/W2140890153","https://openalex.org/W2145576488","https://openalex.org/W2151015649","https://openalex.org/W2190156937","https://openalex.org/W2263246755","https://openalex.org/W2277337617","https://openalex.org/W2310142350","https://openalex.org/W2345042661","https://openalex.org/W2404167154","https://openalex.org/W2414160073","https://openalex.org/W2572003380","https://openalex.org/W2756051650","https://openalex.org/W2760379988","https://openalex.org/W2767910829","https://openalex.org/W2768007622","https://openalex.org/W2790772214","https://openalex.org/W2963204331","https://openalex.org/W3105823702"],"related_works":["https://openalex.org/W4299978068","https://openalex.org/W2950745223","https://openalex.org/W2164189677","https://openalex.org/W4301407218","https://openalex.org/W4296771954","https://openalex.org/W1869870390","https://openalex.org/W2811033119","https://openalex.org/W4245643755","https://openalex.org/W3100108595","https://openalex.org/W2070603889"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"present":[2],"work":[3,61],"departs":[4],"from":[5],"an":[6],"extended":[7],"form":[8],"of":[9,19,69,96,107,123,127,133,145,160,169],"the":[10,20,38,54,67,94,97,108,118,128,131,134,140,143,146,156,162,166,170],"classical":[11,39],"multi-dimensional":[12],"Gross\u2013Pitaevskii":[13,99],"equation,":[14],"which":[15,43],"considers":[16],"fractional":[17,56],"derivatives":[18],"Riesz":[21],"type":[22],"in":[23,59],"space,":[24],"a":[25,84,104],"generalized":[26,55,98,171],"potential":[27],"function":[28],"and":[29,71,115,130,142,148,165],"angular":[30],"momentum":[31],"rotation.":[32],"It":[33,48],"is":[34,49,75,121,158],"well":[35],"known":[36],"that":[37,53,117,155],"system":[40],"possesses":[41,63],"functionals":[42],"are":[44],"preserved":[45],"throughout":[46],"time.":[47],"easy":[50],"to":[51,92,112,153],"check":[52],"model":[57],"considered":[58],"this":[60],"also":[62],"conserved":[64],"quantities,":[65],"whence":[66],"development":[68],"conservative":[70],"efficient":[72],"numerical":[73],"schemes":[74],"pragmatically":[76],"justified.":[77],"Motivated":[78],"by":[79],"these":[80],"facts,":[81],"we":[82,137],"propose":[83],"finite-difference":[85],"method":[86,120,157],"based":[87],"on":[88],"weighted-shifted":[89],"Gr\u00fcnwald":[90],"differences":[91],"approximate":[93],"solutions":[95],"system.":[100,172],"We":[101],"provide":[102,149],"here":[103],"discrete":[105,125],"extension":[106],"uniform":[109],"Sobolev":[110],"inequality":[111],"multiple":[113],"dimensions,":[114],"show":[116,154],"proposed":[119],"capable":[122,159],"preserving":[124,161],"forms":[126],"mass":[129,164],"energy":[132,168],"model.":[135],"Moreover,":[136],"establish":[138],"thoroughly":[139],"stability":[141],"convergence":[144],"technique,":[147],"some":[150],"illustrative":[151],"simulations":[152],"total":[163,167]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2020-01-23T00:00:00"}