{"id":"https://openalex.org/W7204886780","doi":"https://doi.org/10.52754/16948645_2026_1(8)_39","title":"A HYBRID SPECTRAL DEFERRED CORRECTION METHOD WITH PHYSICS-INFORMED NEURAL NETWORK INITIALIZATION","display_name":"A HYBRID SPECTRAL DEFERRED CORRECTION METHOD WITH PHYSICS-INFORMED NEURAL NETWORK INITIALIZATION","publication_year":2026,"publication_date":"2026-05-28","ids":{"openalex":"https://openalex.org/W7204886780","doi":"https://doi.org/10.52754/16948645_2026_1(8)_39"},"language":"en","primary_location":{"id":"doi:10.52754/16948645_2026_1(8)_39","doi":"https://doi.org/10.52754/16948645_2026_1(8)_39","is_oa":true,"landing_page_url":"https://doi.org/10.52754/16948645_2026_1(8)_39","pdf_url":"https://journal.oshsu.kg/index.php/mpht/article/download/4828/2436","source":{"id":"https://openalex.org/S4387288370","display_name":"\u0412\u0435\u0441\u0442\u043d\u0438\u043a \u041e\u0448\u0441\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0424\u0438\u0437\u0438\u043a\u0430 \u0422\u0435\u0445\u043d\u0438\u043a\u0430","issn_l":"1694-8645","issn":["1694-8645"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I186862513","host_organization_name":"Osh State University","host_organization_lineage":["https://openalex.org/I186862513"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0412\u0435\u0441\u0442\u043d\u0438\u043a \u041e\u0448\u0441\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u0424\u0438\u0437\u0438\u043a\u0430. \u0422\u0435\u0445\u043d\u0438\u043a\u0430","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://journal.oshsu.kg/index.php/mpht/article/download/4828/2436","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092556116","display_name":"Ikrom Akramov","orcid":"https://orcid.org/0000-0002-8869-0784","observed_orcids":["https://orcid.org/0000-0002-8869-0784"]},"institutions":[{"id":"https://openalex.org/I3131790217","display_name":"Bukhara State University","ror":"https://ror.org/05k4xnj24","country_code":"UZ","type":"education","lineage":["https://openalex.org/I3131790217"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Ikrom Akramov","raw_affiliation_strings":["\u0411\u0443\u0445\u0430\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u0411\u0443\u0445\u0430\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442","institution_ids":["https://openalex.org/I3131790217"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148850289","display_name":"Tulqin Rasulov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3131790217","display_name":"Bukhara State University","ror":"https://ror.org/05k4xnj24","country_code":"UZ","type":"education","lineage":["https://openalex.org/I3131790217"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Tulqin Rasulov","raw_affiliation_strings":["\u0411\u0443\u0445\u0430\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u0411\u0443\u0445\u0430\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442","institution_ids":["https://openalex.org/I3131790217"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5148922989","display_name":"Dilnora Kurbonova","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3131790217","display_name":"Bukhara State University","ror":"https://ror.org/05k4xnj24","country_code":"UZ","type":"education","lineage":["https://openalex.org/I3131790217"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Dilnora Kurbonova","raw_affiliation_strings":["\u0411\u0443\u0445\u0430\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u0411\u0443\u0445\u0430\u0440\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442","institution_ids":["https://openalex.org/I3131790217"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I3131790217"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":"1(8)","first_page":"39","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.7764000296592712,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.7764000296592712,"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":0.21089999377727509,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.0027000000700354576,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spectral-deferred-correction","display_name":"spectral deferred correction","score":0.9599999785423279},{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.9800000190734863},{"id":"https://openalex.org/keywords/initial-guess","display_name":"initial guess","score":0.6880000233650208},{"id":"https://openalex.org/keywords/ordinary-differential-equations","display_name":"ordinary differential equations","score":0.9319999814033508},{"id":"https://openalex.org/keywords/hybrid-method","display_name":"hybrid algorithm","score":0.5759999752044678},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.9279999732971191},{"id":"https://openalex.org/keywords/high-order-convergence","display_name":"high-order convergence","score":0.8429999947547913},{"id":"https://openalex.org/keywords/quadrature-nodes","display_name":"quadrature nodes","score":0.7459999918937683}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7714999914169312},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6800000071525574},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6236000061035156},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5823000073432922},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5608999729156494},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.366100013256073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.362199991941452},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33239999413490295},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3312999904155731},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27639999985694885},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2615000009536743}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.52754/16948645_2026_1(8)_39","doi":"https://doi.org/10.52754/16948645_2026_1(8)_39","is_oa":true,"landing_page_url":"https://doi.org/10.52754/16948645_2026_1(8)_39","pdf_url":"https://journal.oshsu.kg/index.php/mpht/article/download/4828/2436","source":{"id":"https://openalex.org/S4387288370","display_name":"\u0412\u0435\u0441\u0442\u043d\u0438\u043a \u041e\u0448\u0441\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0424\u0438\u0437\u0438\u043a\u0430 \u0422\u0435\u0445\u043d\u0438\u043a\u0430","issn_l":"1694-8645","issn":["1694-8645"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I186862513","host_organization_name":"Osh State University","host_organization_lineage":["https://openalex.org/I186862513"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0412\u0435\u0441\u0442\u043d\u0438\u043a \u041e\u0448\u0441\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u0424\u0438\u0437\u0438\u043a\u0430. \u0422\u0435\u0445\u043d\u0438\u043a\u0430","raw_type":"journal-article"},{"id":"pmh:oai:journal.oshsu.kg:article/4828","doi":null,"is_oa":true,"landing_page_url":"https://journal.oshsu.kg/index.php/mpht/article/view/4828","pdf_url":null,"source":{"id":"https://openalex.org/S4387288370","display_name":"\u0412\u0435\u0441\u0442\u043d\u0438\u043a \u041e\u0448\u0441\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0424\u0438\u0437\u0438\u043a\u0430 \u0422\u0435\u0445\u043d\u0438\u043a\u0430","issn_l":"1694-8645","issn":["1694-8645"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I186862513","host_organization_name":"Osh State University","host_organization_lineage":["https://openalex.org/I186862513"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1694-8645","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.52754/16948645_2026_1(8)_39","doi":"https://doi.org/10.52754/16948645_2026_1(8)_39","is_oa":true,"landing_page_url":"https://doi.org/10.52754/16948645_2026_1(8)_39","pdf_url":"https://journal.oshsu.kg/index.php/mpht/article/download/4828/2436","source":{"id":"https://openalex.org/S4387288370","display_name":"\u0412\u0435\u0441\u0442\u043d\u0438\u043a \u041e\u0448\u0441\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0424\u0438\u0437\u0438\u043a\u0430 \u0422\u0435\u0445\u043d\u0438\u043a\u0430","issn_l":"1694-8645","issn":["1694-8645"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I186862513","host_organization_name":"Osh State University","host_organization_lineage":["https://openalex.org/I186862513"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0412\u0435\u0441\u0442\u043d\u0438\u043a \u041e\u0448\u0441\u043a\u043e\u0433\u043e \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u0424\u0438\u0437\u0438\u043a\u0430. \u0422\u0435\u0445\u043d\u0438\u043a\u0430","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/W7204886780.pdf","grobid_xml":"https://content.openalex.org/works/W7204886780.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1970213140","https://openalex.org/W1973703726","https://openalex.org/W2049296351","https://openalex.org/W2139494815","https://openalex.org/W2142274086","https://openalex.org/W2293922163","https://openalex.org/W2339583296","https://openalex.org/W2630478408","https://openalex.org/W2899283552","https://openalex.org/W3209298295","https://openalex.org/W4206097460","https://openalex.org/W4250679193","https://openalex.org/W4255754126"],"related_works":["https://openalex.org/W2630478408","https://openalex.org/W2029626973","https://openalex.org/W4396898026","https://openalex.org/W1623046856","https://openalex.org/W7099464778","https://openalex.org/W4240015314","https://openalex.org/W7150824401","https://openalex.org/W3209298295","https://openalex.org/W6908646592","https://openalex.org/W2809898341"],"abstract_inverted_index":{"Spectral":[0],"Deferred":[1],"Correction":[2],"(SDC)":[3],"methods":[4,7],"are":[5],"iterative":[6],"used":[8],"to":[9,102],"solve":[10],"ordinary":[11],"differential":[12],"equations.":[13],"The":[14,91],"SDC":[15,62,71,99],"method":[16,49,93],"can":[17],"achieve":[18,103],"high-order":[19,104],"convergence":[20,35,77],"by":[21],"adjusting":[22],"the":[23,29,39,58,80,96],"initial":[24,40,59],"guess,":[25],"quadrature":[26],"nodes,":[27],"and":[28,72],"number":[30,97],"of":[31,69,79,98],"iterations.":[32,63],"Therefore,":[33],"its":[34],"strongly":[36],"depends":[37],"on":[38],"approximation.":[41],"In":[42],"this":[43],"work,":[44],"we":[45,84],"introduce":[46],"a":[47,52,66,76],"hybrid":[48],"in":[50],"which":[51],"Physics-Informed":[53],"Neural":[54],"Network":[55],"(PINN)":[56],"provides":[57],"guess":[60],"for":[61],"We":[64],"present":[65],"rigorous":[67],"formulation":[68],"both":[70],"PINN,":[73],"along":[74],"with":[75],"analysis":[78],"proposed":[81,92],"method.":[82],"Finally,":[83],"validate":[85],"our":[86],"results":[87],"using":[88],"numerical":[89],"examples.":[90],"significantly":[94],"reduces":[95],"sweeps":[100],"required":[101],"accuracy.":[105]},"counts_by_year":[],"updated_date":"2026-10-25T09:29:13.331239","created_date":"2026-09-02T00:00:00"}
