{"id":"https://openalex.org/W4280495664","doi":"https://doi.org/10.3390/sym14051017","title":"Complexity Reduction Approach for Solving Second Kind of Fredholm Integral Equations","display_name":"Complexity Reduction Approach for Solving Second Kind of Fredholm Integral Equations","publication_year":2022,"publication_date":"2022-05-17","ids":{"openalex":"https://openalex.org/W4280495664","doi":"https://doi.org/10.3390/sym14051017"},"language":"en","primary_location":{"id":"doi:10.3390/sym14051017","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051017","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1017/pdf?version=1652770413","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/2073-8994/14/5/1017/pdf?version=1652770413","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076356026","display_name":"Mohana Sundaram Muthuvalu","orcid":"https://orcid.org/0000-0003-3061-8162"},"institutions":[{"id":"https://openalex.org/I203899302","display_name":"Universiti Teknologi Petronas","ror":"https://ror.org/048g2sh07","country_code":"MY","type":"education","lineage":["https://openalex.org/I203899302"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Mohana Sundaram Muthuvalu","raw_affiliation_strings":["Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia","institution_ids":["https://openalex.org/I203899302"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026158657","display_name":"Elayaraja Aruchunan","orcid":"https://orcid.org/0000-0002-4629-0483"},"institutions":[{"id":"https://openalex.org/I33849332","display_name":"University of Malaya","ror":"https://ror.org/00rzspn62","country_code":"MY","type":"education","lineage":["https://openalex.org/I33849332"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Elayaraja Aruchunan","raw_affiliation_strings":["Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-4629-0483","affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia","institution_ids":["https://openalex.org/I33849332"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101615025","display_name":"Majid Khan Majahar Ali","orcid":"https://orcid.org/0000-0002-5558-5929"},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Majid Khan Majahar Ali","raw_affiliation_strings":["School of Mathematical Sciences, Universiti Sains Malaysia, Gelugor 11800, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Universiti Sains Malaysia, Gelugor 11800, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058474517","display_name":"Jackel Vui Lung Chew","orcid":"https://orcid.org/0000-0002-1195-0955"},"institutions":[{"id":"https://openalex.org/I161371597","display_name":"Universiti of Malaysia Sabah","ror":"https://ror.org/040v70252","country_code":"MY","type":"education","lineage":["https://openalex.org/I161371597"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Jackel Vui Lung Chew","raw_affiliation_strings":["Faculty of Computing and Informatics, Universiti Malaysia Sabah Labuan International Campus, Labuan 87000, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-1195-0955","affiliations":[{"raw_affiliation_string":"Faculty of Computing and Informatics, Universiti Malaysia Sabah Labuan International Campus, Labuan 87000, Malaysia","institution_ids":["https://openalex.org/I161371597"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040610236","display_name":"Andang Sunarto","orcid":"https://orcid.org/0000-0002-4556-602X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andang Sunarto","raw_affiliation_strings":["Tadris Matematika, IAIN Bengkulu, Bengkulu 65144, Indonesia"],"raw_orcid":"https://orcid.org/0000-0002-4556-602X","affiliations":[{"raw_affiliation_string":"Tadris Matematika, IAIN Bengkulu, Bengkulu 65144, Indonesia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018584313","display_name":"Ramoshweu Solomon Lebelo","orcid":"https://orcid.org/0000-0002-8051-1569"},"institutions":[{"id":"https://openalex.org/I129615261","display_name":"Vaal University of Technology","ror":"https://ror.org/05ey7mm31","country_code":"ZA","type":"education","lineage":["https://openalex.org/I129615261"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Ramoshweu Lebelo","raw_affiliation_strings":["Department of Education, Vaal University of Technology, Private Bag X021, Vanderbijlpark 1911, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Education, Vaal University of Technology, Private Bag X021, Vanderbijlpark 1911, South Africa","institution_ids":["https://openalex.org/I129615261"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014369855","display_name":"Jumat Sulaiman","orcid":"https://orcid.org/0000-0002-9538-6588"},"institutions":[{"id":"https://openalex.org/I161371597","display_name":"Universiti of Malaysia Sabah","ror":"https://ror.org/040v70252","country_code":"MY","type":"education","lineage":["https://openalex.org/I161371597"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Jumat Sulaiman","raw_affiliation_strings":["Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Kota Kinabalu 88400, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-9538-6588","affiliations":[{"raw_affiliation_string":"Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Kota Kinabalu 88400, Malaysia","institution_ids":["https://openalex.org/I161371597"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5076356026"],"corresponding_institution_ids":["https://openalex.org/I203899302"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.4588,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61085965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"5","first_page":"1017","last_page":"1017"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9991000294685364,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7176443934440613},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6992965340614319},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.6660054326057434},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6592721343040466},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.6295284032821655},{"id":"https://openalex.org/keywords/fredholm-theory","display_name":"Fredholm theory","score":0.6033499836921692},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.541417121887207},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5158376097679138},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4947023093700409},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4680202901363373},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.46298184990882874},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.45519670844078064},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4141496419906616},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33096832036972046},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3044242560863495},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28200477361679077},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15183857083320618},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07447856664657593}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7176443934440613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6992965340614319},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.6660054326057434},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6592721343040466},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.6295284032821655},{"id":"https://openalex.org/C518188847","wikidata":"https://www.wikidata.org/wiki/Q4455098","display_name":"Fredholm theory","level":4,"score":0.6033499836921692},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.541417121887207},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5158376097679138},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4947023093700409},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4680202901363373},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.46298184990882874},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.45519670844078064},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4141496419906616},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33096832036972046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3044242560863495},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28200477361679077},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15183857083320618},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07447856664657593},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14051017","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051017","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1017/pdf?version=1652770413","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:7d0117c4d3044bc5943dc57fbdce2ab0","is_oa":true,"landing_page_url":"https://doaj.org/article/7d0117c4d3044bc5943dc57fbdce2ab0","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":"Symmetry, Vol 14, Iss 5, p 1017 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/5/1017/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14051017","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14051017","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051017","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1017/pdf?version=1652770413","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":[{"id":"https://openalex.org/G3103181326","display_name":null,"funder_award_id":"015LC0-083","funder_id":"https://openalex.org/F4320329394","funder_display_name":"Yayasan UTP"},{"id":"https://openalex.org/G5938925334","display_name":null,"funder_award_id":"015MC0-033","funder_id":"https://openalex.org/F4320329394","funder_display_name":"Yayasan UTP"}],"funders":[{"id":"https://openalex.org/F4320329394","display_name":"Yayasan UTP","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280495664.pdf","grobid_xml":"https://content.openalex.org/works/W4280495664.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W15735947","https://openalex.org/W166188327","https://openalex.org/W204834058","https://openalex.org/W1525789705","https://openalex.org/W1967818484","https://openalex.org/W1974276128","https://openalex.org/W1976161597","https://openalex.org/W1981891844","https://openalex.org/W1982699088","https://openalex.org/W1991834216","https://openalex.org/W1997472940","https://openalex.org/W2001693767","https://openalex.org/W2002634869","https://openalex.org/W2014208709","https://openalex.org/W2041662036","https://openalex.org/W2080258470","https://openalex.org/W2088953608","https://openalex.org/W2098356380","https://openalex.org/W2110531967","https://openalex.org/W2146944021","https://openalex.org/W2153271180","https://openalex.org/W2183976333","https://openalex.org/W4231406825","https://openalex.org/W4254630587","https://openalex.org/W6606956314","https://openalex.org/W6608434943","https://openalex.org/W6631241840","https://openalex.org/W6644319264","https://openalex.org/W6645651975","https://openalex.org/W6648294697","https://openalex.org/W6651219942","https://openalex.org/W6676458935","https://openalex.org/W7074098084"],"related_works":["https://openalex.org/W2017640945","https://openalex.org/W2493083010","https://openalex.org/W2224175176","https://openalex.org/W2199927350","https://openalex.org/W2067960113","https://openalex.org/W2908503510","https://openalex.org/W3203395433","https://openalex.org/W2972080159","https://openalex.org/W148722298","https://openalex.org/W22811207"],"abstract_inverted_index":{"Initially,":[0],"the":[1,4,19,22,30,51,70,73,93,114,117],"concept":[2],"of":[3,21,32,50,72,76,92,106,116],"complexity":[5,34,101],"reduction":[6,35],"approach":[7,36],"was":[8],"applied":[9,62],"to":[10,63,112],"solve":[11,64],"symmetry":[12],"algebraic":[13],"systems":[14,67],"that":[15],"were":[16],"generated":[17,68],"from":[18,69],"discretization":[20,71],"partial":[23],"differential":[24],"equations.":[25],"Consequently,":[26],"in":[27],"this":[28],"paper,":[29],"effectiveness":[31],"a":[33,82],"based":[37],"on":[38],"half-":[39],"and":[40,57,90,103],"quarter-sweep":[41,58],"iteration":[42],"concepts":[43],"for":[44],"solving":[45],"linear":[46,66,77],"Fredholm":[47,78],"integral":[48,79],"equations":[49,80],"second":[52,74],"kind":[53,75],"is":[54],"investigated.":[55],"Half-":[56],"iterative":[59],"methods":[60,95],"are":[61,96,109],"dense":[65],"using":[81],"repeated":[83],"modified":[84],"trapezoidal":[85],"(RMT)":[86],"scheme.":[87],"The":[88],"formulation":[89],"implementation":[91],"proposed":[94,118],"presented.":[97],"In":[98],"addition,":[99],"computational":[100],"analysis":[102],"numerical":[104],"results":[105],"test":[107],"examples":[108],"also":[110],"included":[111],"verify":[113],"performance":[115],"methods.":[119]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
