{"id":"https://openalex.org/W2011184843","doi":"https://doi.org/10.1080/00207169908804841","title":"Generalized trapezoidal formulas for convection-diffusion equations","display_name":"Generalized trapezoidal formulas for convection-diffusion equations","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2011184843","doi":"https://doi.org/10.1080/00207169908804841","mag":"2011184843"},"language":"en","primary_location":{"id":"doi:10.1080/00207169908804841","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804841","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/A5108385110","display_name":"M. M. Chawla","orcid":null},"institutions":[{"id":"https://openalex.org/I36721946","display_name":"Kuwait University","ror":"https://ror.org/021e5j056","country_code":"KW","type":"education","lineage":["https://openalex.org/I36721946"]}],"countries":["KW"],"is_corresponding":true,"raw_author_name":"M. M. Chawla","raw_affiliation_strings":["Department of Mathematics and Computer Science , Kuwait University , P. O. Box 5969, Safat, Kuwait, 13060"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , Kuwait University , P. O. Box 5969, Safat, Kuwait, 13060","institution_ids":["https://openalex.org/I36721946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078267508","display_name":"M. A. Al-Zanaidi","orcid":null},"institutions":[{"id":"https://openalex.org/I36721946","display_name":"Kuwait University","ror":"https://ror.org/021e5j056","country_code":"KW","type":"education","lineage":["https://openalex.org/I36721946"]}],"countries":["KW"],"is_corresponding":false,"raw_author_name":"M. A. Al-Zanaidi","raw_affiliation_strings":["Department of Mathematics and Computer Science , Kuwait University , P. O. Box 5969, Safat, Kuwait, 13060"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , Kuwait University , P. O. Box 5969, Safat, Kuwait, 13060","institution_ids":["https://openalex.org/I36721946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100768979","display_name":"David J. Evans","orcid":"https://orcid.org/0000-0002-6290-2849"},"institutions":[{"id":"https://openalex.org/I52590639","display_name":"Nottingham Trent University","ror":"https://ror.org/04xyxjd90","country_code":"GB","type":"education","lineage":["https://openalex.org/I52590639"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D. J. Evans","raw_affiliation_strings":["Faculty of Engineering and Computing , Nottingham Trent University , Burton Street, Nottingham, NG1 4BU, UK"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Computing , Nottingham Trent University , Burton Street, Nottingham, NG1 4BU, UK","institution_ids":["https://openalex.org/I52590639"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108385110"],"corresponding_institution_ids":["https://openalex.org/I36721946"],"apc_list":null,"apc_paid":null,"fwci":1.9851,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.85008104,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"72","issue":"2","first_page":"141","last_page":"154"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9984999895095825,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9763000011444092,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.8572266101837158},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.6543155908584595},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.6303668022155762},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5805547833442688},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5326851010322571},{"id":"https://openalex.org/keywords/trapezoidal-rule","display_name":"Trapezoidal rule","score":0.5306200981140137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4985620975494385},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.49495023488998413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48347121477127075},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4768841564655304},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.4743543863296509},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.46628662943840027},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.42373791337013245},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2433682084083557},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.23592227697372437}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8572266101837158},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.6543155908584595},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6303668022155762},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5805547833442688},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5326851010322571},{"id":"https://openalex.org/C78727","wikidata":"https://www.wikidata.org/wiki/Q833293","display_name":"Trapezoidal rule","level":3,"score":0.5306200981140137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4985620975494385},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49495023488998413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48347121477127075},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4768841564655304},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.4743543863296509},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.46628662943840027},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.42373791337013245},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2433682084083557},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.23592227697372437},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169908804841","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804841","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1985248902","https://openalex.org/W2037147834","https://openalex.org/W2040358792","https://openalex.org/W2078886696","https://openalex.org/W2108538926","https://openalex.org/W2315651828","https://openalex.org/W2498216762","https://openalex.org/W3003821699"],"related_works":["https://openalex.org/W2089955609","https://openalex.org/W2349121885","https://openalex.org/W2039299714","https://openalex.org/W2189596786","https://openalex.org/W3111435437","https://openalex.org/W1986291802","https://openalex.org/W4256356077","https://openalex.org/W2109753894","https://openalex.org/W87813395","https://openalex.org/W1968173024"],"abstract_inverted_index":{"We":[0],"describe":[1],"new":[2],"time-integration":[3],"schemes":[4,32,49],"for":[5,11,63],"the":[6,12,17,51,53,57,76,85,88,92,104,108],"linear":[7],"convection-diffusion":[8],"equation":[9],"and":[10,40,42,101],"(viscous)":[13],"Burgers'":[14],"equation,":[15],"employing":[16],"generalized":[18,28],"trapezoidal":[19,29,60],"formulas":[20],"of":[21,69,87,103,110],"Chawla":[22],"et":[23],"al":[24],"[2].":[25],"The":[26,45,67],"obtained":[27],"formula":[30,61],"finite-difference":[31],"(GTF(\u03b1)-FDS)":[33],"are":[34],"second":[35],"order":[36],"in":[37,65,97,107],"both":[38,99],"time":[39],"space":[41],"unconditionally":[43],"stable.":[44],"better":[46],"known":[47],"existing":[48],"employ":[50],"Euler,":[52],"backward":[54],"Euler":[55],"or":[56],"classical":[58],"arithmetic-mean":[59],"(AM-TF)":[62],"integration":[64],"time.":[66],"performance":[68],"our":[70],"present":[71],"GTF(\u03b1)-FDS":[72],"is":[73],"compared":[74],"with":[75],"AM-TF":[77],"scheme":[78],"by":[79,91],"considering":[80],"three":[81],"test":[82],"problems":[83],"wherein":[84],"significance":[86],"role":[89],"played":[90],"parameter":[93],"\u03b1":[94],"becomes":[95],"evident":[96],"providing":[98],"stability":[100],"accuracy":[102],"computed":[105],"solution":[106],"presence":[109],"diffusivity.":[111]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
