{"id":"https://openalex.org/W1978446789","doi":"https://doi.org/10.1016/j.cam.2012.09.010","title":"A meshless method for solving nonlinear two-dimensional integral equations of the second kind on non-rectangular domains using radial basis functions with error analysis","display_name":"A meshless method for solving nonlinear two-dimensional integral equations of the second kind on non-rectangular domains using radial basis functions with error analysis","publication_year":2012,"publication_date":"2012-09-20","ids":{"openalex":"https://openalex.org/W1978446789","doi":"https://doi.org/10.1016/j.cam.2012.09.010","mag":"1978446789"},"language":"en","primary_location":{"id":"doi:10.1016/j.cam.2012.09.010","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2012.09.010","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","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/A5050418984","display_name":"Pouria Assari","orcid":"https://orcid.org/0000-0002-6541-7451"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Pouria Assari","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026886970","display_name":"Hojatollah Adibi","orcid":"https://orcid.org/0000-0002-8167-5020"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hojatollah Adibi","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044309986","display_name":"Mehdi Dehghan","orcid":"https://orcid.org/0000-0002-2573-9755"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mehdi Dehghan","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044309986"],"corresponding_institution_ids":["https://openalex.org/I158248296"],"apc_list":{"value":3040,"currency":"USD","value_usd":3040},"apc_paid":null,"fwci":7.0708,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.96729746,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"239","issue":null,"first_page":"72","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9954000115394592,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9767000079154968,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8425148725509644},{"id":"https://openalex.org/keywords/regularized-meshless-method","display_name":"Regularized meshless method","score":0.7757931351661682},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.6879629492759705},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6565367579460144},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.6324419975280762},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.627567708492279},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5835044384002686},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5696988105773926},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5664858222007751},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5658772587776184},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5606222152709961},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5298343300819397},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4473056197166443},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.4472997188568115},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.41216617822647095},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.37686991691589355},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3626806139945984},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2798525094985962},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21547824144363403},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12642937898635864},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08185562491416931}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8425148725509644},{"id":"https://openalex.org/C177562122","wikidata":"https://www.wikidata.org/wiki/Q7309629","display_name":"Regularized meshless method","level":5,"score":0.7757931351661682},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.6879629492759705},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6565367579460144},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.6324419975280762},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.627567708492279},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5835044384002686},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5696988105773926},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5664858222007751},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5658772587776184},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5606222152709961},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5298343300819397},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4473056197166443},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.4472997188568115},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.41216617822647095},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.37686991691589355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3626806139945984},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2798525094985962},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21547824144363403},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12642937898635864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08185562491416931},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/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/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.cam.2012.09.010","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2012.09.010","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W121978422","https://openalex.org/W186513933","https://openalex.org/W1486164486","https://openalex.org/W1561837382","https://openalex.org/W1590460062","https://openalex.org/W1597405158","https://openalex.org/W1974533927","https://openalex.org/W1977043498","https://openalex.org/W1978142553","https://openalex.org/W1979884183","https://openalex.org/W1982754700","https://openalex.org/W1986177588","https://openalex.org/W1990177855","https://openalex.org/W1992864115","https://openalex.org/W1994582952","https://openalex.org/W1996097836","https://openalex.org/W1996545617","https://openalex.org/W1997574414","https://openalex.org/W2001442636","https://openalex.org/W2009435136","https://openalex.org/W2014208709","https://openalex.org/W2015102866","https://openalex.org/W2024000425","https://openalex.org/W2026593987","https://openalex.org/W2028273853","https://openalex.org/W2033087926","https://openalex.org/W2037848323","https://openalex.org/W2038576504","https://openalex.org/W2045812925","https://openalex.org/W2045935121","https://openalex.org/W2046709860","https://openalex.org/W2047279061","https://openalex.org/W2047877145","https://openalex.org/W2048441106","https://openalex.org/W2052040160","https://openalex.org/W2055023540","https://openalex.org/W2055528045","https://openalex.org/W2059013407","https://openalex.org/W2060819023","https://openalex.org/W2061871845","https://openalex.org/W2063076736","https://openalex.org/W2074797641","https://openalex.org/W2077750600","https://openalex.org/W2078914286","https://openalex.org/W2079929209","https://openalex.org/W2080057507","https://openalex.org/W2082487045","https://openalex.org/W2087623491","https://openalex.org/W2095059673","https://openalex.org/W2095769364","https://openalex.org/W2107699930","https://openalex.org/W2117967613","https://openalex.org/W2119838320","https://openalex.org/W2132717427","https://openalex.org/W2164906883","https://openalex.org/W2166724116","https://openalex.org/W2168857596","https://openalex.org/W2299488510","https://openalex.org/W2494936206","https://openalex.org/W2615324427","https://openalex.org/W4240596267","https://openalex.org/W6607507375","https://openalex.org/W6645174244","https://openalex.org/W6648624309","https://openalex.org/W6649057872","https://openalex.org/W6662120516","https://openalex.org/W6666512442","https://openalex.org/W6670536343","https://openalex.org/W6698167043"],"related_works":["https://openalex.org/W2350605469","https://openalex.org/W2984212906","https://openalex.org/W2012062214","https://openalex.org/W2094296621","https://openalex.org/W1975248355","https://openalex.org/W2170611593","https://openalex.org/W2388359891","https://openalex.org/W2367496310","https://openalex.org/W2501927888","https://openalex.org/W2953818137"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
