{"id":"https://openalex.org/W2073516577","doi":"https://doi.org/10.1137/s0036144595285057","title":"A Similarity Approach to the Numerical Solution of Free Boundary Problems","display_name":"A Similarity Approach to the Numerical Solution of Free Boundary Problems","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2073516577","doi":"https://doi.org/10.1137/s0036144595285057","mag":"2073516577"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144595285057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144595285057","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080837039","display_name":"Riccardo Fazio","orcid":"https://orcid.org/0000-0003-0825-0162"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Riccardo Fazio","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080837039"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4605,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.65047662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"40","issue":"3","first_page":"616","last_page":"635"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9976999759674072,"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 methods for differential equations","score":0.9976999759674072,"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/T10514","display_name":"Numerical methods in engineering","score":0.9968000054359436,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9968000054359436,"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/boundary-value-problem","display_name":"Boundary value problem","score":0.6845223307609558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6539338827133179},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"Free boundary problem","score":0.638541042804718},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.625607430934906},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5547225475311279},{"id":"https://openalex.org/keywords/similarity-solution","display_name":"Similarity solution","score":0.5149246454238892},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.5116310715675354},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.505563497543335},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5044294595718384},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4930517375469208},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4131705164909363},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39898261427879333},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3052489757537842},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21842637658119202},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.12340861558914185},{"id":"https://openalex.org/keywords/boundary-layer","display_name":"Boundary layer","score":0.09757906198501587},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.052750080823898315},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.049474507570266724}],"concepts":[{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6845223307609558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6539338827133179},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.638541042804718},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.625607430934906},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5547225475311279},{"id":"https://openalex.org/C2777282005","wikidata":"https://www.wikidata.org/wiki/Q4056366","display_name":"Similarity solution","level":3,"score":0.5149246454238892},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.5116310715675354},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.505563497543335},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5044294595718384},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4930517375469208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4131705164909363},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39898261427879333},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3052489757537842},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21842637658119202},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.12340861558914185},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.09757906198501587},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.052750080823898315},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.049474507570266724},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036144595285057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144595285057","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W159791876","https://openalex.org/W607196801","https://openalex.org/W1511670827","https://openalex.org/W1521587465","https://openalex.org/W1524253852","https://openalex.org/W1565688698","https://openalex.org/W1568666422","https://openalex.org/W1573927207","https://openalex.org/W1607439417","https://openalex.org/W1963839933","https://openalex.org/W1968373864","https://openalex.org/W1971218752","https://openalex.org/W1971947347","https://openalex.org/W1972348860","https://openalex.org/W1980943062","https://openalex.org/W1986949028","https://openalex.org/W1990132330","https://openalex.org/W1991367612","https://openalex.org/W1993718745","https://openalex.org/W1996009863","https://openalex.org/W2001729937","https://openalex.org/W2002123584","https://openalex.org/W2004203489","https://openalex.org/W2004706442","https://openalex.org/W2006576352","https://openalex.org/W2007917392","https://openalex.org/W2009960521","https://openalex.org/W2010133290","https://openalex.org/W2018891742","https://openalex.org/W2023121979","https://openalex.org/W2023202166","https://openalex.org/W2035164082","https://openalex.org/W2035947984","https://openalex.org/W2039232030","https://openalex.org/W2040064797","https://openalex.org/W2041767124","https://openalex.org/W2042530305","https://openalex.org/W2054417241","https://openalex.org/W2054872897","https://openalex.org/W2060025827","https://openalex.org/W2063446030","https://openalex.org/W2072043211","https://openalex.org/W2075053592","https://openalex.org/W2078644288","https://openalex.org/W2078903387","https://openalex.org/W2079467824","https://openalex.org/W2080403343","https://openalex.org/W2081991462","https://openalex.org/W2082428819","https://openalex.org/W2087581579","https://openalex.org/W2092139299","https://openalex.org/W2101943554","https://openalex.org/W2128024056","https://openalex.org/W2133377911","https://openalex.org/W2141736618","https://openalex.org/W2149557743","https://openalex.org/W2165989366","https://openalex.org/W2170231745","https://openalex.org/W2315787444","https://openalex.org/W2318027604","https://openalex.org/W2331060982","https://openalex.org/W2511343950","https://openalex.org/W2564010961","https://openalex.org/W2773557151","https://openalex.org/W2797256054","https://openalex.org/W3023930659","https://openalex.org/W3149281187","https://openalex.org/W3173176713","https://openalex.org/W4230836784","https://openalex.org/W4235721526","https://openalex.org/W4292170110"],"related_works":["https://openalex.org/W145877682","https://openalex.org/W1548901099","https://openalex.org/W2393913967","https://openalex.org/W2378263446","https://openalex.org/W1991436309","https://openalex.org/W2950745545","https://openalex.org/W1932837131","https://openalex.org/W1984112382","https://openalex.org/W1737185509","https://openalex.org/W4299860049"],"abstract_inverted_index":{"The":[0,33],"aim":[1],"of":[2,16,39,63,75,84,88,106,114,123],"this":[3,89],"work":[4],"is":[5,91],"to":[6,29],"point":[7],"out":[8],"that":[9,53],"within":[10],"a":[11,60],"similarity":[12,61],"approach":[13,109],"some":[14],"classes":[15],"free":[17,40,54],"boundary":[18,41,55,65,76],"value":[19,31,77],"problems":[20,42,56,67,78,113],"governed":[21],"by":[22],"ordinary":[23],"differential":[24],"equations":[25],"can":[26,70],"be":[27,71],"transformed":[28],"initial":[30],"problems.":[32,49],"interest":[34,115],"in":[35,100],"the":[36,85,107],"numerical":[37,119],"solution":[38],"arises":[43],"because":[44],"these":[45],"are":[46,110,116,125],"always":[47],"nonlinear":[48],"Furthermore":[50],"we":[51],"show":[52],"arise":[57],"also":[58],"via":[59],"analysis":[62],"moving":[64],"hyperbolic":[66],"and":[68,95,118],"they":[69],"obtained":[72],"as":[73,104],"approximations":[74],"defined":[79],"on":[80],"infinite":[81],"intervals.":[82],"Most":[83],"theoretical":[86],"content":[87],"survey":[90],"original:":[92],"it":[93],"generalizes":[94],"unifies":[96],"results":[97,120],"already":[98],"available":[99],"literature.":[101],"As":[102],"far":[103],"applications":[105],"proposed":[108],"concerned,":[111],"three":[112],"considered":[117],"for":[121],"each":[122],"them":[124],"reported.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
