{"id":"https://openalex.org/W2016388675","doi":"https://doi.org/10.4236/am.2012.33039","title":"Application of the Hybrid Differential Transform Method to the Nonlinear Equations","display_name":"Application of the Hybrid Differential Transform Method to the Nonlinear Equations","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2016388675","doi":"https://doi.org/10.4236/am.2012.33039","mag":"2016388675"},"language":"en","primary_location":{"id":"doi:10.4236/am.2012.33039","doi":"https://doi.org/10.4236/am.2012.33039","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2012.33039","pdf_url":"https://content.scirp.org/pdf/am20120300008_79855339.pdf","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2016388675"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://content.scirp.org/pdf/am20120300008_79855339.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008240652","display_name":"\u0130nci \u00c7ilingir S\u00fcng\u00fc","orcid":"https://orcid.org/0000-0001-7788-181X","observed_orcids":["https://orcid.org/0000-0001-7788-181X"]},"institutions":[{"id":"https://openalex.org/I227306068","display_name":"Ondokuz May\u0131s University","ror":"https://ror.org/028k5qw24","country_code":"TR","type":"education","lineage":["https://openalex.org/I227306068"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Inci \u00c7ilingir S\u00fcng\u00fc","raw_affiliation_strings":["Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun, Turkey","institution_ids":["https://openalex.org/I227306068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029189700","display_name":"H\u00fcseyin Demir","orcid":"https://orcid.org/0000-0003-3606-878X","observed_orcids":["https://orcid.org/0000-0003-3606-878X"]},"institutions":[{"id":"https://openalex.org/I227306068","display_name":"Ondokuz May\u0131s University","ror":"https://ror.org/028k5qw24","country_code":"TR","type":"education","lineage":["https://openalex.org/I227306068"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"H\u00fcseyin Demir","raw_affiliation_strings":["Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun, Turkey","institution_ids":["https://openalex.org/I227306068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I227306068"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"03","issue":"03","first_page":"246","last_page":"250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.34790000319480896,"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":0.34790000319480896,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.30880001187324524,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.1160999983549118,"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/nonlinear-partial-differential-equations","display_name":"nonlinear partial differential equations","score":0.9729999899864197},{"id":"https://openalex.org/keywords/transient-response","display_name":"transient response","score":0.675000011920929},{"id":"https://openalex.org/keywords/finite-difference-schemes","display_name":"finite difference schemes","score":0.5789999961853027},{"id":"https://openalex.org/keywords/time-discretization","display_name":"time discretization","score":0.5580000281333923},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.6650000214576721},{"id":"https://openalex.org/keywords/nonlinear-initial-value-problems","display_name":"nonlinear initial value problems","score":0.8069999814033508},{"id":"https://openalex.org/keywords/adomian-decomposition-method-comparison","display_name":"Adomian decomposition method comparison","score":0.8579999804496765}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6157609224319458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5950897932052612},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5684932470321655},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5031248927116394},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.46318650245666504},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4548434019088745},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4180283546447754},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.4100780785083771},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3708515763282776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35856756567955017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3354335427284241},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3216543197631836},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4236/am.2012.33039","doi":"https://doi.org/10.4236/am.2012.33039","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2012.33039","pdf_url":"https://content.scirp.org/pdf/am20120300008_79855339.pdf","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.832.9633","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.832.9633","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.scirp.org/journal/PaperDownload.aspx?paperID%3D18099","raw_type":"text"}],"best_oa_location":{"id":"doi:10.4236/am.2012.33039","doi":"https://doi.org/10.4236/am.2012.33039","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2012.33039","pdf_url":"https://content.scirp.org/pdf/am20120300008_79855339.pdf","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","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/W2016388675.pdf","grobid_xml":"https://content.openalex.org/works/W2016388675.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W294519166","https://openalex.org/W1507982735","https://openalex.org/W1975992439","https://openalex.org/W1993496681","https://openalex.org/W1997084329","https://openalex.org/W2009570165","https://openalex.org/W2019193369","https://openalex.org/W2028785883","https://openalex.org/W2049931740","https://openalex.org/W2084396626","https://openalex.org/W2110726881"],"related_works":["https://openalex.org/W2009570165","https://openalex.org/W1902530154","https://openalex.org/W2606954970","https://openalex.org/W4407291157","https://openalex.org/W3105142141","https://openalex.org/W2620406539","https://openalex.org/W2618580818","https://openalex.org/W4206262377","https://openalex.org/W2916606371","https://openalex.org/W2106160456"],"abstract_inverted_index":{"In":[0,117],"this":[1,43,115],"paper,":[2],"a":[3,110],"hybrid":[4,22,61,122,141,162],"method":[5,20,62,95,133],"is":[6,21,45,73,84,96,109,124],"introduced":[7],"briefly":[8],"to":[9,46,86,169],"predict":[10],"the":[11,14,24,48,54,64,80,88,92,103,106,121,127,145,161,171,187],"behavior":[12],"of":[13,42,50,56,67,102,105,114,150,189],"non-linear":[15],"partial":[16,70],"differential":[17,30,51,71,93],"equations.":[18],"The":[19],"in":[23,37,134,185],"sense":[25],"that":[26,160],"different":[27,38,107],"numerical":[28,148],"methods,":[29],"transform":[31,52,94],"and":[32,53,174,181],"finite":[33,57,76,131],"differences,":[34],"are":[35],"used":[36,85,97],"subdomains.":[39],"Our":[40],"aim":[41],"approach":[44,123,163],"combine":[47],"flexibility":[49],"efficiency":[55,104],"differences.":[58],"An":[59],"explicit":[60],"for":[63,98,177],"transient":[65],"response":[66],"inhomogeneous":[68],"nonlinear":[69,190],"equations":[72],"presented;":[74],"applying":[75],"difference":[77,132],"scheme":[78],"on":[79],"fixed":[81],"grid":[82],"size":[83],"approximate":[87],"space":[89],"discretisation,":[90],"whereas":[91],"time":[99,173],"operator.":[100],"Comparison":[101],"approaches":[108],"very":[111],"important":[112,167],"aspect":[113],"study.":[116],"our":[118,140],"test":[119],"cases,":[120],"faster":[125],"than":[126],"corresponding":[128],"highly":[129],"optimized":[130],"two":[135],"dimensional":[136],"computations.":[137],"We":[138],"compared":[139],"approach\u2019s":[142],"results":[143,184],"with":[144],"exact":[146],"and/or":[147],"solutions":[149,188],"PDE":[151],"which":[152],"obtained":[153],"from":[154],"Adomian":[155],"Decomposition":[156],"Method.":[157],"Results":[158],"show":[159],"may":[164],"be":[165],"an":[166],"tool":[168],"reduce":[170],"execution":[172],"memory":[175],"requirements":[176],"large":[178],"scale":[179],"computations":[180],"get":[182],"remarkable":[183],"predicting":[186],"initial":[191],"value":[192],"problems.":[193]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}
