{"id":"https://openalex.org/W1991566581","doi":"https://doi.org/10.1080/00207169708804580","title":"Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of mass","display_name":"Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of mass","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1991566581","doi":"https://doi.org/10.1080/00207169708804580","mag":"1991566581"},"language":"en","primary_location":{"id":"doi:10.1080/00207169708804580","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804580","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/A5039105083","display_name":"Abba B. Gumel","orcid":"https://orcid.org/0000-0002-8413-1248"},"institutions":[{"id":"https://openalex.org/I4210126846","display_name":"Information Technology Laboratory","ror":"https://ror.org/0440c3437","country_code":"US","type":"government","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065","https://openalex.org/I4210126846"]},{"id":"https://openalex.org/I4210117845","display_name":"University Of Information Technology","ror":"https://ror.org/03bxja712","country_code":"MM","type":"education","lineage":["https://openalex.org/I4210117845"]},{"id":"https://openalex.org/I41461413","display_name":"Universiti Malaysia Sarawak","ror":"https://ror.org/05b307002","country_code":"MY","type":"education","lineage":["https://openalex.org/I41461413"]},{"id":"https://openalex.org/I1323252656","display_name":"Information Technology University","ror":"https://ror.org/00ngv8j44","country_code":"PK","type":"education","lineage":["https://openalex.org/I1323252656"]}],"countries":["MM","MY","PK","US"],"is_corresponding":true,"raw_author_name":"A. B. Gumel","raw_affiliation_strings":["\n Faculty of Information Technology","Universiti Malaysia Sarawak;"],"affiliations":[{"raw_affiliation_string":"\n Faculty of Information Technology","institution_ids":["https://openalex.org/I1323252656","https://openalex.org/I4210117845","https://openalex.org/I4210126846"]},{"raw_affiliation_string":"Universiti Malaysia Sarawak;","institution_ids":["https://openalex.org/I41461413"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066742730","display_name":"W.T. Ang","orcid":"https://orcid.org/0000-0003-0637-5578"},"institutions":[{"id":"https://openalex.org/I41461413","display_name":"Universiti Malaysia Sarawak","ror":"https://ror.org/05b307002","country_code":"MY","type":"education","lineage":["https://openalex.org/I41461413"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"W. T. Ang","raw_affiliation_strings":["\n Faculty of Engineering, Universiti Malaysia Sarawak, Kota Samarahan, Sarawak, 94300, Malaysia","Universiti Malaysia Sarawak;"],"affiliations":[{"raw_affiliation_string":"\n Faculty of Engineering, Universiti Malaysia Sarawak, Kota Samarahan, Sarawak, 94300, Malaysia","institution_ids":["https://openalex.org/I41461413"]},{"raw_affiliation_string":"Universiti Malaysia Sarawak;","institution_ids":["https://openalex.org/I41461413"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109129940","display_name":"E. H. Twizell","orcid":null},"institutions":[{"id":"https://openalex.org/I59433898","display_name":"Brunel University of London","ror":"https://ror.org/00dn4t376","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I59433898"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"E. H. Twizell","raw_affiliation_strings":["\n Department of Mathematics and Statistics, Brunel University, Uxbridge, Middlesex, UB8 3PH, England","*Brunel University"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics and Statistics, Brunel University, Uxbridge, Middlesex, UB8 3PH, England","institution_ids":["https://openalex.org/I59433898"]},{"raw_affiliation_string":"*Brunel University","institution_ids":["https://openalex.org/I59433898"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039105083"],"corresponding_institution_ids":["https://openalex.org/I1323252656","https://openalex.org/I41461413","https://openalex.org/I4210117845","https://openalex.org/I4210126846"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.15111516,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"64","issue":"1-2","first_page":"153","last_page":"163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9997000098228455,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9966999888420105,"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.7769911289215088},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6570907235145569},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.5602216124534607},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.5595763325691223},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5549246072769165},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4955223798751831},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.452584832906723},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4371105134487152},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43049898743629456},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36310747265815735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1601705551147461}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.7769911289215088},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6570907235145569},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.5602216124534607},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.5595763325691223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5549246072769165},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4955223798751831},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.452584832906723},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4371105134487152},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43049898743629456},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36310747265815735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1601705551147461},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169708804580","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804580","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":16,"referenced_works":["https://openalex.org/W582600878","https://openalex.org/W1987153023","https://openalex.org/W2005080427","https://openalex.org/W2008541376","https://openalex.org/W2017243500","https://openalex.org/W2018356291","https://openalex.org/W2030228457","https://openalex.org/W2036735138","https://openalex.org/W2040791246","https://openalex.org/W2091053126","https://openalex.org/W2101864692","https://openalex.org/W2154880380","https://openalex.org/W2561757121","https://openalex.org/W2566750562","https://openalex.org/W2600959380","https://openalex.org/W4246241682"],"related_works":["https://openalex.org/W4212973497","https://openalex.org/W1980786482","https://openalex.org/W2360550119","https://openalex.org/W3177208105","https://openalex.org/W2124405825","https://openalex.org/W2165425603","https://openalex.org/W3146633906","https://openalex.org/W2017838066","https://openalex.org/W2149373010","https://openalex.org/W2295182073"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"efficient":[2],"L":[3,100],"0-stable":[4],"parallel":[5,46],"algorithm":[6,20,66,99],"is":[7,21,67],"developed":[8],"for":[9,76],"the":[10,28,33,36,57,74,90],"two-dimensional":[11],"diffusion":[12],"equation":[13],"with":[14,53,89],"non-local":[15],"time-dependent":[16],"boundary":[17,82],"conditions.":[18],"The":[19,65,85],"based":[22],"on":[23,44,69],"subdiagonal":[24],"Pad\u00e9":[25,97],"approximation":[26],"to":[27],"matrix":[29],"exponentials":[30],"arising":[31],"from":[32,73],"use":[34,58],"of":[35,38,59],"method":[37],"lines":[39],"and":[40,81],"may":[41],"be":[42,108,115,123],"implemented":[43],"a":[45],"architecture":[47],"using":[48],"two":[49,70],"processors":[50],"running":[51],"concurrently":[52],"each":[54],"processor":[55],"employing":[56],"tridiagonal":[60],"solvers":[61],"at":[62],"every":[63],"time-step.":[64],"tested":[68],"model":[71],"problems":[72],"literature":[75],"which":[77],"discontinuities":[78],"between":[79],"initial":[80],"conditions":[83],"exist.":[84],"CPU":[86],"times":[87],"together":[88],"associated":[91],"error":[92],"estimates":[93],"are":[94],"compared.":[95],"Keywords:":[96],"approximantparallel":[98],"0-stabilityC.R.Categories:":[101],"G.1.8":[102],"*To":[103,110,118],"whom":[104,111,119],"all":[105,112,120],"correspondence":[106,113,121],"should":[107,114,122],"addressed.":[109,116,124],"Notes":[117]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}