{"id":"https://openalex.org/W4405727035","doi":"https://doi.org/10.3233/faia241400","title":"Overview of Interpolation Finite Difference Methods Enabling Unlimited High-Accuracy Numerical Calculations","display_name":"Overview of Interpolation Finite Difference Methods Enabling Unlimited High-Accuracy Numerical Calculations","publication_year":2024,"publication_date":"2024-12-20","ids":{"openalex":"https://openalex.org/W4405727035","doi":"https://doi.org/10.3233/faia241400"},"language":"en","primary_location":{"id":"doi:10.3233/faia241400","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia241400","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.3233/faia241400","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019133918","display_name":"Tsugio Fukuchi","orcid":"https://orcid.org/0000-0002-5646-8361"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tsugio Fukuchi","raw_affiliation_strings":["Tsubokura Ground-Survey and Design Ltd., Fukushima, Japan"],"raw_orcid":"https://orcid.org/0000-0002-5646-8361","affiliations":[{"raw_affiliation_string":"Tsubokura Ground-Survey and Design Ltd., Fukushima, Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019133918"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.6216692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9918000102043152,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9918000102043152,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9896000027656555,"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":"Differential Equations and Numerical Methods","score":0.9790999889373779,"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/interpolation","display_name":"Interpolation (computer graphics)","score":0.7069761753082275},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6689015626907349},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.6112242341041565},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.555528461933136},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5470401644706726},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4759247601032257},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.47187796235084534},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4686172604560852},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4543251097202301},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4496333599090576},{"id":"https://openalex.org/keywords/numerical-differentiation","display_name":"Numerical differentiation","score":0.4312204122543335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3551744818687439},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27711257338523865},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08087590336799622}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7069761753082275},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6689015626907349},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.6112242341041565},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.555528461933136},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5470401644706726},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4759247601032257},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.47187796235084534},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4686172604560852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4543251097202301},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4496333599090576},{"id":"https://openalex.org/C154181440","wikidata":"https://www.wikidata.org/wiki/Q1683292","display_name":"Numerical differentiation","level":2,"score":0.4312204122543335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3551744818687439},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27711257338523865},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08087590336799622},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/faia241400","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia241400","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.3233/faia241400","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia241400","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W123769205","https://openalex.org/W2016436110","https://openalex.org/W2041746505","https://openalex.org/W2054320306","https://openalex.org/W2136150862","https://openalex.org/W2153024001","https://openalex.org/W2159976235","https://openalex.org/W2510588904","https://openalex.org/W2794833079","https://openalex.org/W2932807069","https://openalex.org/W2945747514","https://openalex.org/W2946389192","https://openalex.org/W3089095475","https://openalex.org/W3110530431","https://openalex.org/W3165233741","https://openalex.org/W4290096735","https://openalex.org/W4307211006","https://openalex.org/W4308996542","https://openalex.org/W4361216962","https://openalex.org/W6885191161","https://openalex.org/W6960165102"],"related_works":["https://openalex.org/W2004744038","https://openalex.org/W1989109250","https://openalex.org/W2330640442","https://openalex.org/W3202647903","https://openalex.org/W2053129613","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W2171402820","https://openalex.org/W4251142058","https://openalex.org/W2962937865"],"abstract_inverted_index":{"There":[0],"are":[1,94],"many":[2],"different":[3],"types":[4],"of":[5,22,71,139,144,161,168,187],"numerical":[6,53,92,118,133,145],"analysis":[7],"for":[8,158],"partial":[9],"differential":[10],"equations.":[11],"Numerical":[12],"methods":[13],"that":[14,91,106,128],"have":[15,25,58],"been":[16,26,60],"studied":[17],"over":[18],"a":[19,68,104,131,136],"long":[20],"period":[21],"time":[23],"and":[24,41,120,179,184,200,208],"used":[27],"in":[28,103],"engineering":[29,86],"practice":[30],"include":[31],"the":[32,50,56,99,108,151,159,164,169,181,194],"finite":[33,37],"difference":[34],"method":[35,39,44],"(FDM),":[36],"element":[38,43],"(FEM),":[40],"boundary":[42,202],"(BEM).":[45],"This":[46,142,174],"paper":[47,175],"focuses":[48],"on":[49],"FDM.":[51],"Conventionally,":[52],"calculations":[54,93,127],"using":[55],"FDM":[57,100,153],"mostly":[59],"performed":[61],"with":[62,135],"second-order":[63],"accuracy.":[64],"It":[65],"usually":[66],"guarantees":[67],"calculation":[69,146],"accuracy":[70,83],"3":[72],"to":[73,80,114,124,130,196],"4":[74],"significant":[75,140],"figures,":[76],"which":[77,189],"is":[78,101,148,163],"considered":[79],"be":[81],"sufficient":[82],"from":[84],"an":[85],"perspective.":[87],"We":[88],"generally":[89],"recognize":[90],"approximate":[95],"calculations.":[96,211],"However,":[97],"when":[98],"generalized":[102],"way":[105],"incorporates":[107],"conventional":[109],"theory,":[110],"it":[111,121],"becomes":[112,122],"possible":[113,123],"perform":[115,126],"unlimitedly":[116],"high-accuracy":[117,206],"calculations,":[119,207],"easily":[125],"converge":[129],"theoretical":[132,182],"solution":[134],"certain":[137],"number":[138],"figures.":[141],"type":[143],"system":[147],"defined":[149],"as":[150],"interpolation":[152],"(IFDM).":[154],"The":[155],"essential":[156],"requirement":[157],"establishment":[160],"IFDM":[162],"algebraic":[165],"polynomial":[166],"approximation":[167],"(real":[170],"number)":[171],"analytic":[172],"function.":[173],"describes":[176],"this":[177],"concept":[178],"outlines":[180],"features":[183],"computational":[185],"examples":[186],"IFDM,":[188],"has":[190],"three":[191],"characteristics:":[192],"(i)":[193],"ability":[195],"handle":[197],"arbitrary":[198,201],"domains":[199],"conditions,":[203],"(ii)":[204],"unlimited":[205],"(iii)":[209],"high-speed":[210]},"counts_by_year":[],"updated_date":"2026-02-06T02:01:19.302388","created_date":"2025-10-10T00:00:00"}