{"id":"https://openalex.org/W2017435993","doi":"https://doi.org/10.1080/00207160108805120","title":"An Efficient Double Legendre Spectral Method for Parabolic and Elliptic Partial Differential Equations","display_name":"An Efficient Double Legendre Spectral Method for Parabolic and Elliptic Partial Differential Equations","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2017435993","doi":"https://doi.org/10.1080/00207160108805120","mag":"2017435993"},"language":"en","primary_location":{"id":"doi:10.1080/00207160108805120","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160108805120","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5016529266","display_name":"E. H. Doha","orcid":"https://orcid.org/0000-0002-7781-6871"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"E. H. Doha","raw_affiliation_strings":["Department of Mathematics, Faculty of Science , Cairo University , Giza, Egypt","Department of Mathematics, Faculty of Science , Cairo University , Giza , Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science , Cairo University , Giza, Egypt","institution_ids":["https://openalex.org/I145487455"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science , Cairo University , Giza , Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025853995","display_name":"F. M. R. Al-Kholi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. M. R. Al-Kholi","raw_affiliation_strings":["Department of Mathematics , Girl' College of Education , Jeddah, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Girl' College of Education , Jeddah, Saudi Arabia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016529266"],"corresponding_institution_ids":["https://openalex.org/I145487455"],"apc_list":null,"apc_paid":null,"fwci":3.4162,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.9169112,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"78","issue":"3","first_page":"413","last_page":"432"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.991100013256073,"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"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.991100013256073,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9901000261306763,"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/T10514","display_name":"Numerical methods in engineering","score":0.9883999824523926,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8432592153549194},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.6701018810272217},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.6462746858596802},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6176696419715881},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.6008890867233276},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5494850277900696},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5421655178070068},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5325974822044373},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5227817893028259},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.4768085181713104},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.46824371814727783},{"id":"https://openalex.org/keywords/exponential-integrator","display_name":"Exponential integrator","score":0.4362364113330841},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.38191360235214233},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.34536612033843994},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.1982673704624176},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.18778300285339355},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08017244935035706}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8432592153549194},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.6701018810272217},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.6462746858596802},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6176696419715881},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.6008890867233276},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5494850277900696},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5421655178070068},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5325974822044373},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5227817893028259},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.4768085181713104},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.46824371814727783},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.4362364113330841},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.38191360235214233},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.34536612033843994},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.1982673704624176},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.18778300285339355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08017244935035706},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160108805120","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160108805120","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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":23,"referenced_works":["https://openalex.org/W1482513797","https://openalex.org/W1607071030","https://openalex.org/W1980998752","https://openalex.org/W1984700819","https://openalex.org/W1988546126","https://openalex.org/W1989768884","https://openalex.org/W1997701847","https://openalex.org/W2006983615","https://openalex.org/W2009466983","https://openalex.org/W2014172170","https://openalex.org/W2036494998","https://openalex.org/W2068207468","https://openalex.org/W2075454166","https://openalex.org/W2134572726","https://openalex.org/W2166245316","https://openalex.org/W2408478130","https://openalex.org/W2569133694","https://openalex.org/W2798788284","https://openalex.org/W3035235874","https://openalex.org/W4242475175","https://openalex.org/W4248145103","https://openalex.org/W4301046466","https://openalex.org/W7081428392"],"related_works":["https://openalex.org/W3020098708","https://openalex.org/W2006263304","https://openalex.org/W3147000368","https://openalex.org/W2357676173","https://openalex.org/W2582405793","https://openalex.org/W1990866326","https://openalex.org/W1590810315","https://openalex.org/W4312705771","https://openalex.org/W4289812957","https://openalex.org/W3127383398"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,20],"double":[3,94],"Legendre":[4,95],"spectral":[5,96],"methods":[6,79],"that":[7],"allow":[8],"the":[9,14,24,49,68,90],"efficient":[10],"approximate":[11],"solution":[12],"for":[13,48,98],"parabolic":[15],"partial":[16],"differential":[17,32,46],"equations":[18,33,47,102],"in":[19],"square":[21],"subject":[22],"to":[23,42,76],"most":[25],"general":[26],"inhomo-geneous":[27],"mixed":[28],"boundary":[29,36],"conditions.":[30],"The":[31],"with":[34,87],"their":[35],"and":[37,63,100],"initial":[38],"conditions":[39],"are":[40,55,64,103],"reduced":[41],"systems":[43,54],"of":[44,74,89],"ordinary":[45],"time-dependent":[50],"expansion":[51],"coefficients.":[52],"These":[53],"greatly":[56],"simplified":[57],"by":[58,66],"using":[59,67],"tensor":[60],"matrix":[61],"algebra,":[62],"solved":[65],"step-by-step":[69],"method.":[70],"One":[71],"numerical":[72],"application":[73],"how":[75],"use":[77],"these":[78],"is":[80],"described.":[81],"Numerical":[82],"results":[83],"obtained":[84],"compare":[85],"favorably":[86],"those":[88],"analytical":[91],"solution.":[92],"Accurate":[93],"approximations":[97],"Poisson'":[99],"Helmholtz'":[101],"also":[104],"noted.":[105]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
