{"id":"https://openalex.org/W2614142768","doi":"https://doi.org/10.1007/s10915-017-0598-1","title":"Radial Basis Function Methods for the Rosenau Equation and Other Higher Order PDEs","display_name":"Radial Basis Function Methods for the Rosenau Equation and Other Higher Order PDEs","publication_year":2017,"publication_date":"2017-11-15","ids":{"openalex":"https://openalex.org/W2614142768","doi":"https://doi.org/10.1007/s10915-017-0598-1","mag":"2614142768"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-017-0598-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-017-0598-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10915-017-0598-1.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10915-017-0598-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087388598","display_name":"Ali Safdari-Vaighani","orcid":"https://orcid.org/0000-0003-1603-2798"},"institutions":[{"id":"https://openalex.org/I200432940","display_name":"Allameh Tabataba'i University","ror":"https://ror.org/02cc4gc68","country_code":"IR","type":"education","lineage":["https://openalex.org/I200432940"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Safdari-Vaighani","raw_affiliation_strings":["Department of Mathematical and Computer Sciences, Allameh Tabataba\u2019i University, Tehran, Iran","Department of Mathematical and Computer Sciences, Allameh Tabataba'i University, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computer Sciences, Allameh Tabataba\u2019i University, Tehran, Iran","institution_ids":["https://openalex.org/I200432940"]},{"raw_affiliation_string":"Department of Mathematical and Computer Sciences, Allameh Tabataba'i University, Tehran, Iran","institution_ids":["https://openalex.org/I200432940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072928406","display_name":"Elisabeth Larsson","orcid":"https://orcid.org/0000-0003-1154-9587"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Elisabeth Larsson","raw_affiliation_strings":["Department of Information Technology, Uppsala University, Uppsala, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Information Technology, Uppsala University, Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036702793","display_name":"Alfa Heryudono","orcid":"https://orcid.org/0000-0001-7531-2891"},"institutions":[{"id":"https://openalex.org/I100633361","display_name":"University of Massachusetts Dartmouth","ror":"https://ror.org/00fzmm222","country_code":"US","type":"education","lineage":["https://openalex.org/I100633361"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alfa Heryudono","raw_affiliation_strings":["Department of Mathematics, University of Massachusetts Dartmouth, Dartmouth, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Massachusetts Dartmouth, Dartmouth, MA, USA","institution_ids":["https://openalex.org/I100633361"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072928406"],"corresponding_institution_ids":["https://openalex.org/I123387679"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.0927,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.84890592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"75","issue":"3","first_page":"1555","last_page":"1580"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9962999820709229,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9922000169754028,"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/radial-basis-function","display_name":"Radial basis function","score":0.7880538702011108},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7221046686172485},{"id":"https://openalex.org/keywords/moving-least-squares","display_name":"Moving least squares","score":0.5773410797119141},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5179585218429565},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4961491525173187},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.4585961401462555},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4574330449104309},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4569852650165558},{"id":"https://openalex.org/keywords/meshfree-methods","display_name":"Meshfree methods","score":0.4466882348060608},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42953455448150635},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42554834485054016},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3813017010688782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3207930326461792},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.29812610149383545},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.2192421853542328},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2182813286781311},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19910761713981628}],"concepts":[{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.7880538702011108},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7221046686172485},{"id":"https://openalex.org/C2780580100","wikidata":"https://www.wikidata.org/wiki/Q6927143","display_name":"Moving least squares","level":2,"score":0.5773410797119141},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5179585218429565},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4961491525173187},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.4585961401462555},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4574330449104309},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4569852650165558},{"id":"https://openalex.org/C162835735","wikidata":"https://www.wikidata.org/wiki/Q14866890","display_name":"Meshfree methods","level":3,"score":0.4466882348060608},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42953455448150635},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42554834485054016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3813017010688782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3207930326461792},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29812610149383545},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2192421853542328},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2182813286781311},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19910761713981628},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10915-017-0598-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-017-0598-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10915-017-0598-1.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:DiVA.org:uu-334532","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-334532","pdf_url":null,"source":{"id":"https://openalex.org/S4306402042","display_name":"Uppsala University Publications (Uppsala University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123387679","host_organization_name":"Uppsala University","host_organization_lineage":["https://openalex.org/I123387679"],"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":"","raw_type":"Article in journal"}],"best_oa_location":{"id":"doi:10.1007/s10915-017-0598-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-017-0598-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10915-017-0598-1.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1652824100","display_name":null,"funder_award_id":"1552238","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7416101847","display_name":null,"funder_award_id":"235730","funder_id":"https://openalex.org/F4320338368","funder_display_name":"FP7 People: Marie-Curie Actions"},{"id":"https://openalex.org/G7889267731","display_name":"FEM-RBF: A geometrically flexible, efficient numerical solution technique for partial differential equations with mixed regularity","funder_award_id":"235730","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7984001250","display_name":null,"funder_award_id":"1552238","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320338368","display_name":"FP7 People: Marie-Curie Actions","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2614142768.pdf","grobid_xml":"https://content.openalex.org/works/W2614142768.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W92678590","https://openalex.org/W618867606","https://openalex.org/W1490180844","https://openalex.org/W1558122728","https://openalex.org/W1577242818","https://openalex.org/W1812894164","https://openalex.org/W1964990804","https://openalex.org/W1967998814","https://openalex.org/W2015699529","https://openalex.org/W2015725973","https://openalex.org/W2017047018","https://openalex.org/W2019470769","https://openalex.org/W2020462115","https://openalex.org/W2029469957","https://openalex.org/W2036048988","https://openalex.org/W2039402388","https://openalex.org/W2044309282","https://openalex.org/W2051847605","https://openalex.org/W2055623556","https://openalex.org/W2075151302","https://openalex.org/W2082100828","https://openalex.org/W2088822475","https://openalex.org/W2123805128","https://openalex.org/W2136431693","https://openalex.org/W2137606648","https://openalex.org/W2157763285","https://openalex.org/W2319797753","https://openalex.org/W2321428294","https://openalex.org/W2403418182","https://openalex.org/W2560552443","https://openalex.org/W2625275472","https://openalex.org/W2999792156","https://openalex.org/W3120739866","https://openalex.org/W4244829582"],"related_works":["https://openalex.org/W2084120563","https://openalex.org/W2140171609","https://openalex.org/W1968883776","https://openalex.org/W3015671932","https://openalex.org/W256613907","https://openalex.org/W2441614350","https://openalex.org/W1991688655","https://openalex.org/W2382174623","https://openalex.org/W2801875094","https://openalex.org/W2126147105"],"abstract_inverted_index":{"Meshfree":[0],"methods":[1,156,217],"based":[2],"on":[3],"radial":[4],"basis":[5],"function":[6],"(RBF)":[7],"approximation":[8,87],"are":[9,21,39,110],"of":[10,15,28,57,66,73,120,141,165,173,214],"interest":[11],"for":[12,43,52,146,184],"numerical":[13,151],"solution":[14,65],"partial":[16],"differential":[17],"equations":[18],"because":[19],"they":[20,32,38,50],"flexible":[22],"with":[23,45,78,103,171,207],"respect":[24],"to":[25,61,99,210,218],"the":[26,29,64,67,91,96,121,147,160,163,166,174,185,189,192,212,215],"geometry":[27],"computational":[30],"domain,":[31],"can":[33,82,143],"provide":[34],"high":[35,139],"order":[36,140],"convergence,":[37],"not":[40],"more":[41],"complicated":[42],"problems":[44],"many":[46],"space":[47,116],"dimensions":[48],"and":[49,95,114,130,202],"allow":[51],"local":[53],"refinement.":[54],"The":[55,118,133,150],"aim":[56],"this":[58],"paper":[59],"is":[60,126,169,195],"show":[62,153],"that":[63,137,154,172],"Rosenau":[68,148,193],"equation,":[69],"as":[70],"an":[71,74,104,204],"example":[72],"initial-boundary":[75],"value":[76],"problem":[77,194],"multiple":[79],"boundary":[80],"conditions,":[81],"be":[83,144],"implemented":[84,111],"using":[85],"RBF":[86,105,122,167,186],"methods.":[88,187],"We":[89],"extend":[90],"fictitious":[92,123],"point":[93,124],"method":[94,98,125],"resampling":[97],"work":[100],"in":[101,112,198,203],"combination":[102],"collocation":[106],"method.":[107],"Both":[108],"approaches":[109,168],"one":[113],"two":[115],"dimensions.":[117],"accuracy":[119,164,183],"analyzed":[127],"partly":[128,131],"theoretically":[129],"numerically.":[132],"error":[134],"estimates":[135],"indicate":[136],"a":[138,199],"convergence":[142],"achieved":[145],"equation.":[149],"experiments":[152],"both":[155,197],"perform":[157],"well.":[158],"In":[159,188],"one-dimensional":[161],"case,":[162,191],"compared":[170],"corresponding":[175],"pseudospectral":[176],"methods,":[177],"showing":[178],"similar":[179],"or":[180],"slightly":[181],"better":[182],"two-dimensional":[190],"solved":[196],"square":[200],"domain":[201,206],"irregular":[205,220],"smooth":[208],"boundary,":[209],"illustrate":[211],"capability":[213],"RBF-based":[216],"handle":[219],"geometries.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}