{"id":"https://openalex.org/W2955538032","doi":"https://doi.org/10.1201/9780429081385-58","title":"Refining Existing Numerical Integration Methods","display_name":"Refining Existing Numerical Integration Methods","publication_year":2019,"publication_date":"2019-04-29","ids":{"openalex":"https://openalex.org/W2955538032","doi":"https://doi.org/10.1201/9780429081385-58","mag":"2955538032"},"language":"en","primary_location":{"id":"doi:10.1201/9780429081385-58","doi":"https://doi.org/10.1201/9780429081385-58","is_oa":false,"landing_page_url":"https://doi.org/10.1201/9780429081385-58","pdf_url":null,"source":{"id":"https://openalex.org/S4306463075","display_name":"CRC Press eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320584","host_organization_name":"CRC Press","host_organization_lineage":["https://openalex.org/P4310320584","https://openalex.org/P4310320547"],"host_organization_lineage_names":["CRC Press","Taylor & Francis"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004)","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2949503595","display_name":"International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004)"},"type":"conference-paper","is_traditional":true,"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":null,"display_name":"P. Johnson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Johnson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012697287","display_name":"Krishna Busawon","orcid":"https://orcid.org/0000-0002-9058-0824","observed_orcids":["https://orcid.org/0000-0002-9058-0824"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Busawon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068043644","display_name":"S. Danaher","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Danaher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1307947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"234","last_page":"238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary 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 Solvers for Ordinary 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/T13806","display_name":"Mathematical and Computational Methods","score":0.00039999998989515007,"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/T13286","display_name":"Modeling and Simulation Systems","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/adaptive-step-size","display_name":"adaptive step size","score":0.8029999732971191},{"id":"https://openalex.org/keywords/ordinary-differential-equations","display_name":"ordinary differential equations","score":0.9990000128746033},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.9190000295639038},{"id":"https://openalex.org/keywords/heun-method","display_name":"Heun method","score":0.9670000076293945},{"id":"https://openalex.org/keywords/runge-kutta-methods","display_name":"Runge-Kutta method","score":0.9850000143051147},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.6480000019073486},{"id":"https://openalex.org/keywords/numerical-accuracy","display_name":"numerical accuracy","score":0.4189999997615814}],"concepts":[{"id":"https://openalex.org/C60044698","wikidata":"https://www.wikidata.org/wiki/Q1283324","display_name":"Refining (metallurgy)","level":2,"score":0.8682316541671753},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4543142318725586},{"id":"https://openalex.org/C21880701","wikidata":"https://www.wikidata.org/wiki/Q2144042","display_name":"Process engineering","level":1,"score":0.38203945755958557},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.2384999692440033},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.18172380328178406},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.16664361953735352}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1201/9780429081385-58","doi":"https://doi.org/10.1201/9780429081385-58","is_oa":false,"landing_page_url":"https://doi.org/10.1201/9780429081385-58","pdf_url":null,"source":{"id":"https://openalex.org/S4306463075","display_name":"CRC Press eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320584","host_organization_name":"CRC Press","host_organization_lineage":["https://openalex.org/P4310320584","https://openalex.org/P4310320547"],"host_organization_lineage_names":["CRC Press","Taylor & Francis"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004)","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2144375544"],"related_works":["https://openalex.org/W6936599855","https://openalex.org/W1996761005","https://openalex.org/W7091570159","https://openalex.org/W1979993784","https://openalex.org/W760877222","https://openalex.org/W7095278312","https://openalex.org/W2076750256","https://openalex.org/W7128048660","https://openalex.org/W3022020271","https://openalex.org/W1848218854"],"abstract_inverted_index":{"In":[0],"this":[1,77],"paper":[2],"we":[3],"present":[4],"a":[5],"refinement":[6],"to":[7,32,47],"the":[8,25,33,48,53,69,84,104,118,126,134,140],"single-step":[9,93,105,142],"numerical":[10,30],"methods":[11,110],"of":[12,35,64,117],"solving":[13],"ordinary":[14],"differential":[15],"equations":[16],"(ODEs).":[17],"We":[18],"propose":[19],"an":[20,36],"adaptive":[21,78,113],"algorithm":[22,39,79,136],"for":[23,122],"generating":[24],"step":[26],"length":[27],"between":[28],"successive":[29],"approximations":[31,46],"solution":[34,49,54],"ODE.":[37],"The":[38],"is":[40,56,60,71,74,97,120,131],"designed":[41],"such":[42],"that":[43,133],"more":[44],"accurate":[45],"are":[50],"made":[51],"when":[52,68],"gradient":[55,70],"high,":[57],"whilst":[58],"accuracy":[59],"dropped":[61],"in":[62],"favour":[63],"economising":[65],"computation":[66],"effort":[67],"low.":[72],"It":[73],"demonstrated":[75,132],"how":[76],"can":[80],"be":[81],"incorporated":[82],"into":[83],"forward":[85],"Euler":[86],"method":[87,114],"as":[88,90],"well":[89],"all":[91],"other":[92],"methods.":[94,143],"An":[95],"example":[96],"studied":[98],"and":[99,108,128],"simulations":[100,119,127],"carried":[101,121],"out":[102],"comparing":[103],"Euler,":[106],"Heun":[107],"Runge-Kutta":[109],"with":[111],"their":[112],"counterparts.":[115],"Analysis":[116],"each":[123],"case.":[124],"Through":[125],"analysis":[129],"it":[130],"proposed":[135],"does":[137],"indeed":[138],"refine":[139],"existing":[141]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2019-07-12T00:00:00"}