{"id":"https://openalex.org/W2948936768","doi":"https://doi.org/10.1137/19m1267441","title":"A Sparse Spectral Method for Volterra Integral Equations Using Orthogonal Polynomials on the Triangle","display_name":"A Sparse Spectral Method for Volterra Integral Equations Using Orthogonal Polynomials on the Triangle","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2948936768","doi":"https://doi.org/10.1137/19m1267441","mag":"2948936768"},"language":"en","primary_location":{"id":"doi:10.1137/19m1267441","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1267441","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://export.arxiv.org/pdf/1906.03907","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064837586","display_name":"Timon S. Gutleb","orcid":"https://orcid.org/0000-0002-8239-2372"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Timon S. Gutleb","raw_affiliation_strings":["Imperial College London"],"affiliations":[{"raw_affiliation_string":"Imperial College London","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010027385","display_name":"Sheehan Olver","orcid":"https://orcid.org/0000-0001-6920-0826"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sheehan Olver","raw_affiliation_strings":["Imperial College London"],"affiliations":[{"raw_affiliation_string":"Imperial College London","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064837586"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":0.27606185,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.42683929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"58","issue":"3","first_page":"1993","last_page":"2018"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9966999888420105,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9883999824523926,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.7845001220703125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7409783601760864},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.6980859041213989},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.6555039882659912},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5835976004600525},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5247438549995422},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.5212305784225464},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5185495018959045},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.4540998041629791},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4387560784816742},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4190247058868408},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3457973003387451},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3321388363838196},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27698609232902527},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14476540684700012}],"concepts":[{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.7845001220703125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7409783601760864},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.6980859041213989},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.6555039882659912},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5835976004600525},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5247438549995422},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.5212305784225464},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5185495018959045},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.4540998041629791},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4387560784816742},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4190247058868408},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3457973003387451},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3321388363838196},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27698609232902527},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14476540684700012},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/19m1267441","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1267441","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"mag:2948936768","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1906.03907","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/79585","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/79585","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2018","raw_type":"Journal Article"},{"id":"doi:10.48550/arxiv.1906.03907","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1906.03907","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"mag:2948936768","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1906.03907","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W351768996","https://openalex.org/W1480637530","https://openalex.org/W1491593102","https://openalex.org/W1517932056","https://openalex.org/W1543326485","https://openalex.org/W1550150926","https://openalex.org/W1567668233","https://openalex.org/W1593505867","https://openalex.org/W1678272269","https://openalex.org/W1740105476","https://openalex.org/W1972534508","https://openalex.org/W1977486208","https://openalex.org/W1988742704","https://openalex.org/W2013943932","https://openalex.org/W2019552700","https://openalex.org/W2020254850","https://openalex.org/W2021719174","https://openalex.org/W2038992763","https://openalex.org/W2043669521","https://openalex.org/W2109453208","https://openalex.org/W2119337797","https://openalex.org/W2120575449","https://openalex.org/W2130010995","https://openalex.org/W2130694104","https://openalex.org/W2133064603","https://openalex.org/W2134526557","https://openalex.org/W2143933531","https://openalex.org/W2161644951","https://openalex.org/W2171692351","https://openalex.org/W2245233932","https://openalex.org/W2253496911","https://openalex.org/W2276306181","https://openalex.org/W2480359983","https://openalex.org/W2540371815","https://openalex.org/W2585014300","https://openalex.org/W2616864018","https://openalex.org/W2768435914","https://openalex.org/W2773734884","https://openalex.org/W2779980829","https://openalex.org/W2785663543","https://openalex.org/W2912669820","https://openalex.org/W2962716964","https://openalex.org/W2962785284","https://openalex.org/W2962910852","https://openalex.org/W2963567562","https://openalex.org/W2964338872","https://openalex.org/W2990035746","https://openalex.org/W3016019514","https://openalex.org/W3101769428","https://openalex.org/W3198318828"],"related_works":["https://openalex.org/W2998947547","https://openalex.org/W2972587304","https://openalex.org/W3186586247","https://openalex.org/W2067072893","https://openalex.org/W865932272","https://openalex.org/W124929775","https://openalex.org/W3101769428","https://openalex.org/W3109089832","https://openalex.org/W135499075","https://openalex.org/W2003771343","https://openalex.org/W2257550218","https://openalex.org/W2964177109","https://openalex.org/W2349720946","https://openalex.org/W3038144070","https://openalex.org/W2053870969","https://openalex.org/W2351410330","https://openalex.org/W3183392843","https://openalex.org/W2049119935","https://openalex.org/W2356597129","https://openalex.org/W2563352603"],"abstract_inverted_index":{"We":[0,75],"introduce":[1],"and":[2,40,61,81],"analyse":[3],"a":[4,20,30,48],"sparse":[5],"spectral":[6],"method":[7,52],"for":[8,78],"the":[9,26,51,59,86],"solution":[10],"of":[11,25,50,58],"Volterra":[12,27,55],"integral":[13,56],"equations":[14,57],"using":[15],"bivariate":[16],"orthogonal":[17],"polynomials":[18],"on":[19,29,53,89],"triangle":[21],"domain.":[22],"The":[23,43],"sparsity":[24],"operator":[28],"weighted":[31],"Jacobi":[32],"basis":[33],"is":[34,45],"used":[35],"to":[36],"achieve":[37],"high":[38],"efficiency":[39],"exponential":[41],"convergence.":[42],"discussion":[44],"followed":[46],"by":[47],"demonstration":[49],"example":[54],"first":[60,80],"second":[62,82],"kind":[63,83],"with":[64,91],"known":[65],"analytic":[66],"solutions":[67],"as":[68,70],"well":[69],"an":[71],"application-oriented":[72],"numerical":[73],"experiment.":[74],"prove":[76],"convergence":[77],"both":[79],"problems,":[84],"where":[85],"former":[87],"builds":[88],"connections":[90],"Toeplitz":[92],"operators.":[93]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
