{"id":"https://openalex.org/W4383876879","doi":"https://doi.org/10.3389/fams.2023.1214022","title":"Study of the stability of a meshless generalized finite difference scheme applied to the wave equation","display_name":"Study of the stability of a meshless generalized finite difference scheme applied to the wave equation","publication_year":2023,"publication_date":"2023-07-11","ids":{"openalex":"https://openalex.org/W4383876879","doi":"https://doi.org/10.3389/fams.2023.1214022"},"language":"en","primary_location":{"id":"doi:10.3389/fams.2023.1214022","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2023.1214022","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2023.1214022/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/articles/10.3389/fams.2023.1214022/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090487308","display_name":"Gerardo Tinoco-Guerrero","orcid":"https://orcid.org/0000-0003-3119-770X"},"institutions":[{"id":"https://openalex.org/I173755004","display_name":"Universidad Michoacana de San Nicol\u00e1s de Hidalgo","ror":"https://ror.org/00z0kq074","country_code":"MX","type":"education","lineage":["https://openalex.org/I173755004"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Gerardo Tinoco-Guerrero","raw_affiliation_strings":["Civil Engineering Faculty, Universidad Michoacana de San Nicol\u00e1s de Hidalgo, Morelia, Michoac\u00e1n, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Civil Engineering Faculty, Universidad Michoacana de San Nicol\u00e1s de Hidalgo, Morelia, Michoac\u00e1n, Mexico","institution_ids":["https://openalex.org/I173755004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112957357","display_name":"Francisco Javier Dom\u00ednguez-Mota","orcid":null},"institutions":[{"id":"https://openalex.org/I173755004","display_name":"Universidad Michoacana de San Nicol\u00e1s de Hidalgo","ror":"https://ror.org/00z0kq074","country_code":"MX","type":"education","lineage":["https://openalex.org/I173755004"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Francisco Javier Dom\u00ednguez-Mota","raw_affiliation_strings":["Faculty of Physics and Mathematics, UMSNH, Morelia, Michoac\u00e1n, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics and Mathematics, UMSNH, Morelia, Michoac\u00e1n, Mexico","institution_ids":["https://openalex.org/I173755004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042571671","display_name":"Jos\u00e9 A. Guzm\u00e1n-Torres","orcid":"https://orcid.org/0000-0002-9309-9390"},"institutions":[{"id":"https://openalex.org/I173755004","display_name":"Universidad Michoacana de San Nicol\u00e1s de Hidalgo","ror":"https://ror.org/00z0kq074","country_code":"MX","type":"education","lineage":["https://openalex.org/I173755004"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Alberto Guzm\u00e1n-Torres","raw_affiliation_strings":["Civil Engineering Faculty, Universidad Michoacana de San Nicol\u00e1s de Hidalgo, Morelia, Michoac\u00e1n, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Civil Engineering Faculty, Universidad Michoacana de San Nicol\u00e1s de Hidalgo, Morelia, Michoac\u00e1n, Mexico","institution_ids":["https://openalex.org/I173755004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015437810","display_name":"Ricardo Rom\u00e1n-Guti\u00e9rrez","orcid":"https://orcid.org/0000-0001-8521-9391"},"institutions":[{"id":"https://openalex.org/I173755004","display_name":"Universidad Michoacana de San Nicol\u00e1s de Hidalgo","ror":"https://ror.org/00z0kq074","country_code":"MX","type":"education","lineage":["https://openalex.org/I173755004"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Ricardo Rom\u00e1n-Guti\u00e9rrez","raw_affiliation_strings":["Faculty of Physics and Mathematics, UMSNH, Morelia, Michoac\u00e1n, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics and Mathematics, UMSNH, Morelia, Michoac\u00e1n, Mexico","institution_ids":["https://openalex.org/I173755004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058680028","display_name":"Jos\u00e9 Gerardo Tinoco-Ruiz","orcid":"https://orcid.org/0000-0002-0866-4798"},"institutions":[{"id":"https://openalex.org/I173755004","display_name":"Universidad Michoacana de San Nicol\u00e1s de Hidalgo","ror":"https://ror.org/00z0kq074","country_code":"MX","type":"education","lineage":["https://openalex.org/I173755004"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Gerardo Tinoco-Ruiz","raw_affiliation_strings":["Faculty of Physics and Mathematics, UMSNH, Morelia, Michoac\u00e1n, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics and Mathematics, UMSNH, Morelia, Michoac\u00e1n, Mexico","institution_ids":["https://openalex.org/I173755004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5090487308"],"corresponding_institution_ids":["https://openalex.org/I173755004"],"apc_list":{"value":1150,"currency":"USD","value_usd":1150},"apc_paid":{"value":1150,"currency":"USD","value_usd":1150},"fwci":0.4004,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.54240463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"9","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9980999827384949,"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/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.7632066011428833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6937234401702881},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5904024243354797},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5552119612693787},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.512787401676178},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5126732587814331},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5126239657402039},{"id":"https://openalex.org/keywords/central-differencing-scheme","display_name":"Central differencing scheme","score":0.48062294721603394},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.43078354001045227},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4208889603614807},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.4166645407676697},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4142477512359619},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.37673017382621765},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3730524182319641},{"id":"https://openalex.org/keywords/finite-difference-coefficient","display_name":"Finite difference coefficient","score":0.260636568069458},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20861297845840454},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.12206315994262695},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06399261951446533}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7632066011428833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6937234401702881},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5904024243354797},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5552119612693787},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.512787401676178},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5126732587814331},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5126239657402039},{"id":"https://openalex.org/C157866214","wikidata":"https://www.wikidata.org/wiki/Q17006341","display_name":"Central differencing scheme","level":5,"score":0.48062294721603394},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.43078354001045227},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4208889603614807},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.4166645407676697},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4142477512359619},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.37673017382621765},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3730524182319641},{"id":"https://openalex.org/C108268861","wikidata":"https://www.wikidata.org/wiki/Q1747602","display_name":"Finite difference coefficient","level":4,"score":0.260636568069458},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20861297845840454},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.12206315994262695},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06399261951446533},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3389/fams.2023.1214022","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2023.1214022","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2023.1214022/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4bbb04e1f3614a0e955689de2f537ca3","is_oa":true,"landing_page_url":"https://doaj.org/article/4bbb04e1f3614a0e955689de2f537ca3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Applied Mathematics and Statistics, Vol 9 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fams.2023.1214022","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2023.1214022","pdf_url":"https://www.frontiersin.org/articles/10.3389/fams.2023.1214022/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322900","display_name":"Universidad Michoacana de San Nicol\u00e1s de Hidalgo","ror":"https://ror.org/00z0kq074"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383876879.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W613955682","https://openalex.org/W1964116178","https://openalex.org/W1968642437","https://openalex.org/W1970012262","https://openalex.org/W1999769834","https://openalex.org/W2010592405","https://openalex.org/W2021036023","https://openalex.org/W2047319386","https://openalex.org/W2159752342","https://openalex.org/W2165304903","https://openalex.org/W2188761561","https://openalex.org/W2498216762","https://openalex.org/W2731242594","https://openalex.org/W2954111110","https://openalex.org/W2963645054","https://openalex.org/W3005239502","https://openalex.org/W3136989454","https://openalex.org/W3190511610","https://openalex.org/W4220971172","https://openalex.org/W4244063180","https://openalex.org/W4294553380","https://openalex.org/W4319783555","https://openalex.org/W4360943379"],"related_works":["https://openalex.org/W2018573070","https://openalex.org/W1994822208","https://openalex.org/W2311000004","https://openalex.org/W2389517732","https://openalex.org/W2124138615","https://openalex.org/W3099809193","https://openalex.org/W2141533127","https://openalex.org/W1977574797","https://openalex.org/W2133469542","https://openalex.org/W2348610871"],"abstract_inverted_index":{"When":[0],"designing":[1],"and":[2,33,53,111],"implementing":[3],"numerical":[4,78],"schemes,":[5],"it":[6],"is":[7,118,126,143],"imperative":[8],"to":[9,31,46,76,108,139],"consider":[10],"the":[11,14,24,47,68,77,81,104,123,131,152,164,174,177],"stability":[12,25,69,94,132,175],"of":[13,26,70,80,87,161,176],"applied":[15,30,75],"methods.":[16],"Prior":[17],"research":[18,39,186],"has":[19,40],"presented":[20,96,134],"different":[21],"results":[22],"for":[23,89,168,184],"generalized":[27,43,71],"finite-difference":[28,44],"methods":[29],"advection":[32],"diffusion":[34],"equations.":[35],"In":[36],"recent":[37],"years,":[38],"explored":[41],"a":[42,65,182],"approach":[45],"advection-diffusion":[48],"equation":[49],"solved":[50,84],"on":[51,67,85],"non-rectangular":[52],"highly":[54,90,169],"irregular":[55,91,170],"regions":[56],"using":[57],"convex,":[58],"logically":[59],"rectangular":[60],"grids.":[61],"This":[62],"paper":[63,137],"presents":[64],"study":[66,180],"finite":[72],"difference":[73],"schemes":[74],"solution":[79],"wave":[82,165],"equation,":[83,166],"clouds":[86],"points":[88],"domains.":[92,171],"The":[93,114,155],"analysis":[95],"in":[97,135,148,187],"this":[98,136,179,188],"work":[99],"provides":[100,181],"significant":[101],"insights":[102],"into":[103],"proper":[105],"discretizations":[106],"needed":[107],"obtain":[109],"stable":[110,120,128],"satisfactory":[112],"results.":[113],"proposed":[115,153,156],"explicit":[116],"scheme":[117,125,141,157],"conditionally":[119],",":[121],"while":[122],"implicit":[124],"unconditionally":[127],".":[129],"Notably,":[130],"analyses":[133],"apply":[138],"any":[140],"which":[142],"at":[144],"least":[145],"second":[146],"order":[147],"space,":[149],"not":[150],"just":[151],"approach.":[154],"offers":[158],"effective":[159],"means":[160],"numerically":[162],"solving":[163],"particularly":[167],"By":[172],"demonstrating":[173],"scheme,":[178],"foundation":[183],"further":[185],"area.":[189]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-27T09:02:27.158192","created_date":"2025-10-10T00:00:00"}
