{"id":"https://openalex.org/W4206500008","doi":"https://doi.org/10.3390/sym14010115","title":"Fast Computation of Highly Oscillatory ODE Problems: Applications in High-Frequency Communication Circuits","display_name":"Fast Computation of Highly Oscillatory ODE Problems: Applications in High-Frequency Communication Circuits","publication_year":2022,"publication_date":"2022-01-09","ids":{"openalex":"https://openalex.org/W4206500008","doi":"https://doi.org/10.3390/sym14010115"},"language":"en","primary_location":{"id":"doi:10.3390/sym14010115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010115","pdf_url":"https://www.mdpi.com/2073-8994/14/1/115/pdf?version=1641781029","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/2073-8994/14/1/115/pdf?version=1641781029","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080153198","display_name":"Sakhi Zaman","orcid":"https://orcid.org/0000-0001-5446-0609"},"institutions":[{"id":"https://openalex.org/I90610274","display_name":"University of Engineering and Technology Peshawar","ror":"https://ror.org/00p034093","country_code":"PK","type":"education","lineage":["https://openalex.org/I90610274"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sakhi Zaman","raw_affiliation_strings":["Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5446-0609","affiliations":[{"raw_affiliation_string":"Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I90610274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015854563","display_name":"Latif U. Khan","orcid":"https://orcid.org/0000-0002-7678-6949"},"institutions":[{"id":"https://openalex.org/I90610274","display_name":"University of Engineering and Technology Peshawar","ror":"https://ror.org/00p034093","country_code":"PK","type":"education","lineage":["https://openalex.org/I90610274"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Latif Ullah Khan","raw_affiliation_strings":["Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I90610274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102919173","display_name":"Irshad Hussain","orcid":"https://orcid.org/0000-0001-9103-1803"},"institutions":[{"id":"https://openalex.org/I90610274","display_name":"University of Engineering and Technology Peshawar","ror":"https://ror.org/00p034093","country_code":"PK","type":"education","lineage":["https://openalex.org/I90610274"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Irshad Hussain","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-9103-1803","affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, University of Engineering and Technology Peshawar, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I90610274"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072790317","display_name":"Lucian Mihet\u2010Popa","orcid":"https://orcid.org/0000-0002-4556-2774"},"institutions":[{"id":"https://openalex.org/I19923696","display_name":"\u00d8stfold University College","ror":"https://ror.org/04gf7fp41","country_code":"NO","type":"education","lineage":["https://openalex.org/I19923696"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Lucian Mihet-Popa","raw_affiliation_strings":["Faculty of Information Technology, Engineering and Economics, Oestfold University College, 1757 Halden, Norway"],"raw_orcid":"https://orcid.org/0000-0002-4556-2774","affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Engineering and Economics, Oestfold University College, 1757 Halden, Norway","institution_ids":["https://openalex.org/I19923696"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072790317","https://openalex.org/A5102919173"],"corresponding_institution_ids":["https://openalex.org/I19923696","https://openalex.org/I90610274"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.0009,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.96227364,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"1","first_page":"115","last_page":"115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9990000128746033,"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":0.9990000128746033,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9976999759674072,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9975000023841858,"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":0.7118710279464722},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6266852617263794},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5260565280914307},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5144007802009583},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5068755745887756},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4901917576789856},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.4491831064224243},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4476798176765442},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4265877604484558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3679848313331604},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.32370927929878235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11086630821228027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7118710279464722},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6266852617263794},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5260565280914307},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5144007802009583},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5068755745887756},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4901917576789856},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.4491831064224243},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4476798176765442},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4265877604484558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3679848313331604},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32370927929878235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11086630821228027},{"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},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym14010115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010115","pdf_url":"https://www.mdpi.com/2073-8994/14/1/115/pdf?version=1641781029","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:53cd45aa6a7c4508b0ac4902ff11dfb6","is_oa":true,"landing_page_url":"https://doaj.org/article/53cd45aa6a7c4508b0ac4902ff11dfb6","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 1, p 115 (2022)","raw_type":"article"},{"id":"pmh:oai:hiof.brage.unit.no:11250/2989949","is_oa":true,"landing_page_url":"https://hdl.handle.net/11250/2989949","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"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":"14","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/1/115/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14010115","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/sym14010115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010115","pdf_url":"https://www.mdpi.com/2073-8994/14/1/115/pdf?version=1641781029","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/W4206500008.pdf","grobid_xml":"https://content.openalex.org/works/W4206500008.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W203847317","https://openalex.org/W1488691889","https://openalex.org/W1966478028","https://openalex.org/W1967566051","https://openalex.org/W1989695190","https://openalex.org/W1993967870","https://openalex.org/W2001786567","https://openalex.org/W2005961899","https://openalex.org/W2019984076","https://openalex.org/W2021297049","https://openalex.org/W2021815773","https://openalex.org/W2025363317","https://openalex.org/W2027942036","https://openalex.org/W2031291316","https://openalex.org/W2046470632","https://openalex.org/W2059961698","https://openalex.org/W2106720685","https://openalex.org/W2112945849","https://openalex.org/W2133672042","https://openalex.org/W2165677267","https://openalex.org/W2463002925","https://openalex.org/W2553291899","https://openalex.org/W2990919202","https://openalex.org/W2996602018","https://openalex.org/W3176543478","https://openalex.org/W6655995036","https://openalex.org/W6679602675"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2958348684","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W2059261580","https://openalex.org/W4362679168"],"abstract_inverted_index":{"The":[0,85,108,141,179,210],"paper":[1],"demonstrates":[2],"symmetric":[3,143],"integral":[4,102,139,145],"operator":[5],"and":[6,13,51,93,114,119,199],"interpolation":[7],"based":[8],"numerical":[9,217],"approximations":[10],"for":[11],"linear":[12,174,181],"nonlinear":[14,158],"ordinary":[15],"differential":[16],"equations":[17,33],"(ODEs)":[18],"with":[19,130,165],"oscillatory":[20,29,65,71,83,118,131,138,144,167,182],"factor":[21],"x\u2032=\u03c8(x)+\u03c7\u03c9(t),":[22],"where":[23],"the":[24,64,68,101,105,125,152,157,161,188,193,216],"function":[25,91],"\u03c7\u03c9(t)":[26],"is":[27,111,134,147,170,184],"an":[28,166],"forcing":[30,132,168],"term.":[31],"These":[32],"appear":[34],"in":[35,42,215],"a":[36,173],"variety":[37],"of":[38,70,76,104,160,192],"computational":[39,45],"problems":[40,164],"occurring":[41],"Fourier":[43],"analysis,":[44,47],"harmonic":[46],"fluid":[48],"dynamics,":[49],"electromagnetics,":[50],"quantum":[52],"mechanics.":[53],"Classical":[54],"methods":[55,59,77,195,204],"such":[56,205],"as":[57,206],"Runge\u2013Kutta":[58],"etc.":[60,209],"fail":[61],"to":[62,80,99],"approximate":[63,81,116],"ODEs":[66],"due":[67],"existence":[69],"term":[72,133,169],"\u03c7\u03c9(t).":[73],"Two":[74],"types":[75],"are":[78,97,196,213],"presented":[79],"highly":[82,117,137],"ODEs.":[84],"first":[86],"method":[87],"uses":[88],"radial":[89],"basis":[90],"interpolation,":[92],"then":[94,148,185],"quadrature":[95],"rules":[96],"used":[98],"evaluate":[100],"part":[103],"solution":[106],"equation.":[107,140],"second":[109],"approach":[110],"more":[112,197],"generic":[113],"can":[115],"nonoscillatory":[120],"initial":[121,127,162],"value":[122,128,163],"problems.":[123],"Accordingly,":[124],"first-order":[126],"problem":[129,183],"transformed":[135,142],"into":[136,172],"equation":[146],"evaluated":[149],"numerically":[150],"by":[151,187],"Levin":[153,189],"collocation":[154],"method.":[155,190],"Finally,":[156],"form":[159,175],"converted":[171],"using":[176],"Bernoulli\u2019s":[177],"transformation.":[178],"resulting":[180],"computed":[186],"Results":[191],"proposed":[194],"reliable":[198],"accurate":[200],"than":[201],"some":[202],"state-of-the-art":[203],"asymptotic":[207],"method,":[208],"improved":[211],"results":[212],"shown":[214],"section.":[218]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":8}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}