{"id":"https://openalex.org/W2914679279","doi":"https://doi.org/10.3390/sym11020257","title":"Numerical Simulation of Partial Differential Equations via Local Meshless Method","display_name":"Numerical Simulation of Partial Differential Equations via Local Meshless Method","publication_year":2019,"publication_date":"2019-02-19","ids":{"openalex":"https://openalex.org/W2914679279","doi":"https://doi.org/10.3390/sym11020257","mag":"2914679279"},"language":"en","primary_location":{"id":"doi:10.3390/sym11020257","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020257","pdf_url":"https://www.mdpi.com/2073-8994/11/2/257/pdf?version=1550566645","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/2/257/pdf?version=1550566645","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089160568","display_name":"Imtiaz Ahmad","orcid":"https://orcid.org/0000-0002-4023-3293"},"institutions":[{"id":"https://openalex.org/I4210142599","display_name":"University of Swabi","ror":"https://ror.org/04ez8az68","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210142599"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Imtiaz Ahmad","raw_affiliation_strings":["Department of Mathematics, University of Swabi, Khyber Pakhtunkhwa 23200, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Swabi, Khyber Pakhtunkhwa 23200, Pakistan","institution_ids":["https://openalex.org/I4210142599"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049665961","display_name":"Muhammad Riaz","orcid":"https://orcid.org/0000-0001-8115-9168"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Riaz","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052265070","display_name":"Muhammad Ayaz","orcid":"https://orcid.org/0000-0001-9027-5590"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Ayaz","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087585103","display_name":"Muhammad Arif","orcid":"https://orcid.org/0000-0003-1484-7643"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Arif","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040226905","display_name":"Saeed Islam","orcid":"https://orcid.org/0000-0001-5263-4871"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saeed Islam","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036720066","display_name":"Poom Kumam","orcid":"https://orcid.org/0000-0002-5463-4581"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I60837268","display_name":"King Mongkut's University of Technology Thonburi","ror":"https://ror.org/0057ax056","country_code":"TH","type":"education","lineage":["https://openalex.org/I60837268"]}],"countries":["TH","TW"],"is_corresponding":true,"raw_author_name":"Poom Kumam","raw_affiliation_strings":["Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand","KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand","KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand","KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I4210126829","https://openalex.org/I184693016"]},{"raw_affiliation_string":"KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand","institution_ids":["https://openalex.org/I60837268"]},{"raw_affiliation_string":"KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand","institution_ids":["https://openalex.org/I60837268"]},{"raw_affiliation_string":"KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand","institution_ids":["https://openalex.org/I60837268"]},{"raw_affiliation_string":"KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand","institution_ids":["https://openalex.org/I60837268"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5036720066"],"corresponding_institution_ids":["https://openalex.org/I184693016","https://openalex.org/I4210126829","https://openalex.org/I60837268"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.9193,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.89697105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"11","issue":"2","first_page":"257","last_page":"257"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9884999990463257,"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/T12293","display_name":"Dam Engineering and Safety","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/regularized-meshless-method","display_name":"Regularized meshless method","score":0.894716739654541},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7143222093582153},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6533433198928833},{"id":"https://openalex.org/keywords/meshfree-methods","display_name":"Meshfree methods","score":0.6294592618942261},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6068978309631348},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.5433787107467651},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.49967098236083984},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.4937148988246918},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.4831656813621521},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4797983467578888},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.46723753213882446},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4607359766960144},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35229164361953735},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3308061957359314},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3198609948158264},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3007064461708069},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.22251448035240173},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07925817370414734},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.07746663689613342}],"concepts":[{"id":"https://openalex.org/C177562122","wikidata":"https://www.wikidata.org/wiki/Q7309629","display_name":"Regularized meshless method","level":5,"score":0.894716739654541},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7143222093582153},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6533433198928833},{"id":"https://openalex.org/C162835735","wikidata":"https://www.wikidata.org/wiki/Q14866890","display_name":"Meshfree methods","level":3,"score":0.6294592618942261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6068978309631348},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.5433787107467651},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.49967098236083984},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.4937148988246918},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.4831656813621521},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4797983467578888},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.46723753213882446},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4607359766960144},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35229164361953735},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3308061957359314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3198609948158264},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3007064461708069},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.22251448035240173},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07925817370414734},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.07746663689613342},{"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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":2,"locations":[{"id":"doi:10.3390/sym11020257","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020257","pdf_url":"https://www.mdpi.com/2073-8994/11/2/257/pdf?version=1550566645","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6f8eee574afd4b09b6418ef884203080","is_oa":true,"landing_page_url":"https://doaj.org/article/6f8eee574afd4b09b6418ef884203080","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 2, p 257 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11020257","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020257","pdf_url":"https://www.mdpi.com/2073-8994/11/2/257/pdf?version=1550566645","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2914679279.pdf","grobid_xml":"https://content.openalex.org/works/W2914679279.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W158727854","https://openalex.org/W395181431","https://openalex.org/W1974982502","https://openalex.org/W1977070309","https://openalex.org/W1979227627","https://openalex.org/W1984123162","https://openalex.org/W1998646770","https://openalex.org/W2001323141","https://openalex.org/W2017253015","https://openalex.org/W2026497497","https://openalex.org/W2030459145","https://openalex.org/W2031607863","https://openalex.org/W2032873066","https://openalex.org/W2034568860","https://openalex.org/W2039249518","https://openalex.org/W2040280650","https://openalex.org/W2045578252","https://openalex.org/W2051916099","https://openalex.org/W2057855801","https://openalex.org/W2060015237","https://openalex.org/W2071452568","https://openalex.org/W2077791698","https://openalex.org/W2080439207","https://openalex.org/W2080728047","https://openalex.org/W2081668429","https://openalex.org/W2084450780","https://openalex.org/W2089256538","https://openalex.org/W2094566788","https://openalex.org/W2094884329","https://openalex.org/W2097997105","https://openalex.org/W2116074698","https://openalex.org/W2132775908","https://openalex.org/W2181604708","https://openalex.org/W2183395219","https://openalex.org/W2254592078","https://openalex.org/W2298217228","https://openalex.org/W2330906940","https://openalex.org/W2561980341","https://openalex.org/W2582932698","https://openalex.org/W2607070827","https://openalex.org/W2620121926","https://openalex.org/W2904136109","https://openalex.org/W4244934557","https://openalex.org/W6658619968","https://openalex.org/W6663534172","https://openalex.org/W6685793609","https://openalex.org/W6686318227","https://openalex.org/W6697875479"],"related_works":["https://openalex.org/W2984212906","https://openalex.org/W1975248355","https://openalex.org/W2012062214","https://openalex.org/W2089665536","https://openalex.org/W2355497163","https://openalex.org/W3021318023","https://openalex.org/W2084117867","https://openalex.org/W2362859999","https://openalex.org/W2391276610","https://openalex.org/W2741285735"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"numerical":[3],"simulation":[4],"of":[5,46,62,74,99,129],"one,":[6],"two":[7],"and":[8,28,50,91,112,118,126],"three":[9],"dimensional":[10],"partial":[11],"differential":[12],"equations":[13],"(PDEs)":[14],"are":[15,33,54,122,133],"obtained":[16,60],"by":[17,67],"local":[18,27,76],"meshless":[19,30,77,107],"method":[20,78,108,132],"using":[21],"radial":[22],"basis":[23],"functions":[24],"(RBFs).":[25],"Both":[26,110],"global":[29,106],"collocation":[31],"procedures":[32],"used":[34,55],"for":[35,56],"spatial":[36,57],"discretization,":[37],"which":[38],"convert":[39],"the":[40,75,88,97,105,130],"given":[41],"PDEs":[42],"into":[43],"a":[44],"system":[45,61],"ODEs.":[47],"Multiquadric,":[48],"Gaussian":[49],"inverse":[51],"quadratic":[52],"RBFs":[53],"discretization.":[58],"The":[59,71],"ODEs":[63],"has":[64],"been":[65],"solved":[66],"different":[68],"time":[69],"integrators.":[70],"salient":[72],"feature":[73],"(LMM)":[79],"is":[80],"that":[81],"it":[82],"does":[83],"not":[84],"require":[85],"mesh":[86],"in":[87],"problem":[89],"domain":[90],"also":[92],"far":[93],"less":[94],"sensitive":[95],"to":[96,104],"variation":[98],"shape":[100],"parameter":[101],"as":[102],"compared":[103],"(GMM).":[109],"rectangular":[111,114],"non":[113],"domains":[115],"with":[116],"uniform":[117],"scattered":[119],"nodal":[120],"points":[121],"considered.":[123],"Accuracy,":[124],"efficacy":[125],"ease":[127],"implementation":[128],"proposed":[131],"shown":[134],"via":[135],"test":[136],"problems.":[137]},"counts_by_year":[{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":3}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}
