{"id":"https://openalex.org/W2036830564","doi":"https://doi.org/10.1080/00207160500069888","title":"Non-linear singular systems using RK\u2013Butcher algorithms","display_name":"Non-linear singular systems using RK\u2013Butcher algorithms","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2036830564","doi":"https://doi.org/10.1080/00207160500069888","mag":"2036830564"},"language":"en","primary_location":{"id":"doi:10.1080/00207160500069888","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160500069888","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/A5103518679","display_name":"D. J. Evans","orcid":null},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David J. Evans","raw_affiliation_strings":["Parallelism, Algorithms and Architectures Research Centre, Department of Computer Science, Loughborough University, Loughborough, LE11 3TU, UK","Parallelism, Algorithms and Architectures Research Centre, Department of Computer Science , Loughborough University , Loughborough, LE11 3TU, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Parallelism, Algorithms and Architectures Research Centre, Department of Computer Science, Loughborough University, Loughborough, LE11 3TU, UK","institution_ids":["https://openalex.org/I143804889"]},{"raw_affiliation_string":"Parallelism, Algorithms and Architectures Research Centre, Department of Computer Science , Loughborough University , Loughborough, LE11 3TU, UK","institution_ids":["https://openalex.org/I143804889"]}]},{"author_position":"middle","author":{"id":null,"display_name":"K. Murugesan","orcid":null},"institutions":[{"id":"https://openalex.org/I122964287","display_name":"National Institute of Technology Tiruchirappalli","ror":"https://ror.org/047x65e68","country_code":"IN","type":"education","lineage":["https://openalex.org/I122964287"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"K. Murugesan","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015, Tamil Nadu, India","Department of Mathematics , National Institute of Technology , Tiruchirappalli, 620 015, Tamil Nadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015, Tamil Nadu, India","institution_ids":["https://openalex.org/I122964287"]},{"raw_affiliation_string":"Department of Mathematics , National Institute of Technology , Tiruchirappalli, 620 015, Tamil Nadu, India","institution_ids":["https://openalex.org/I122964287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050763659","display_name":"S. Sekar","orcid":"https://orcid.org/0009-0006-8687-8851"},"institutions":[{"id":"https://openalex.org/I122964287","display_name":"National Institute of Technology Tiruchirappalli","ror":"https://ror.org/047x65e68","country_code":"IN","type":"education","lineage":["https://openalex.org/I122964287"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. Sekar","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015, Tamil Nadu, India","Department of Mathematics , National Institute of Technology , Tiruchirappalli, 620 015, Tamil Nadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015, Tamil Nadu, India","institution_ids":["https://openalex.org/I122964287"]},{"raw_affiliation_string":"Department of Mathematics , National Institute of Technology , Tiruchirappalli, 620 015, Tamil Nadu, India","institution_ids":["https://openalex.org/I122964287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101408344","display_name":"Hyun\u2010Min Kim","orcid":"https://orcid.org/0000-0002-4728-3621"},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hyun-Min Kim","raw_affiliation_strings":["Department of Mathematics, Pusan National University, Pusan, 609-735, Republic of Korea","Department of Mathematics, Pusan National University, Pusan 609-735, Republic of Korea#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pusan National University, Pusan, 609-735, Republic of Korea","institution_ids":["https://openalex.org/I4921948"]},{"raw_affiliation_string":"Department of Mathematics, Pusan National University, Pusan 609-735, Republic of Korea#TAB#","institution_ids":["https://openalex.org/I4921948"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I122964287"],"apc_list":null,"apc_paid":null,"fwci":0.8607,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72091738,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"83","issue":"1","first_page":"131","last_page":"142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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":0.9994000196456909,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7121936678886414},{"id":"https://openalex.org/keywords/butcher","display_name":"Butcher","score":0.606768786907196},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5423676371574402},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4441296458244324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3769274652004242},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3450945019721985},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1931045651435852},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18797406554222107}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7121936678886414},{"id":"https://openalex.org/C2779094126","wikidata":"https://www.wikidata.org/wiki/Q329737","display_name":"Butcher","level":2,"score":0.606768786907196},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5423676371574402},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4441296458244324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3769274652004242},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3450945019721985},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1931045651435852},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18797406554222107},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160500069888","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160500069888","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":26,"referenced_works":["https://openalex.org/W1535122194","https://openalex.org/W1596150805","https://openalex.org/W1980148094","https://openalex.org/W1990511557","https://openalex.org/W2007140202","https://openalex.org/W2008007187","https://openalex.org/W2022483586","https://openalex.org/W2024899160","https://openalex.org/W2028611859","https://openalex.org/W2037989464","https://openalex.org/W2040308813","https://openalex.org/W2044537258","https://openalex.org/W2048302708","https://openalex.org/W2072922264","https://openalex.org/W2084749963","https://openalex.org/W2086340522","https://openalex.org/W2086657800","https://openalex.org/W2088682873","https://openalex.org/W2107442606","https://openalex.org/W2128952455","https://openalex.org/W2144375544","https://openalex.org/W2164544589","https://openalex.org/W2484971506","https://openalex.org/W2997123088","https://openalex.org/W4243689439","https://openalex.org/W4292929576"],"related_works":["https://openalex.org/W3087756247","https://openalex.org/W3084900569","https://openalex.org/W2507640626","https://openalex.org/W1986548664","https://openalex.org/W2388101034","https://openalex.org/W2490741836","https://openalex.org/W3169805072","https://openalex.org/W2741644504","https://openalex.org/W2980030500","https://openalex.org/W2914096973"],"abstract_inverted_index":{"The":[0,14,106],"Runge\u2013Kutta":[1],"(RK)\u2013Butcher":[2],"algorithm":[3,63,108],"is":[4,54,64,140],"used":[5],"to":[6,66,99],"study":[7],"time-invariant":[8,49,130],"and":[9,33,50,81,90,117,131],"time-varying":[10,51,132],"non-linear":[11,44,72,136],"singular":[12,45,73,137],"systems.":[13,74],"results":[15],"(discrete":[16],"solutions)":[17],"obtained":[18,59,122],"using":[19,60,113],"the":[20,25,39,43,48,57,61,67,71,78,101,118],"RK":[21],"method":[22],"based":[23],"on":[24],"arithmetic":[26],"mean":[27],"(RKAM),":[28],"single-term":[29],"Walsh":[30],"series":[31],"(STWS)":[32],"RK\u2013Butcher":[34,62,82,107],"algorithms":[35,83],"are":[36,84,93],"compared":[37],"with":[38],"exact":[40,68,91],"solutions":[41,69,92],"of":[42,70,103,126,144],"systems":[46],"for":[47,77,88,123,128,134],"cases.":[52],"It":[53],"found":[55],"that":[56],"solution":[58,119],"closer":[65],"Stability":[75],"regions":[76],"RKAM,":[79],"STWS":[80],"presented.":[85],"Error":[86],"graphs":[87],"discrete":[89],"presented":[94],"in":[95],"a":[96,114],"graphical":[97],"form":[98],"highlight":[100],"efficiency":[102],"this":[104,145],"method.":[105],"can":[109,120],"easily":[110],"be":[111,121],"implemented":[112],"digital":[115],"computer":[116],"any":[124],"length":[125],"time":[127],"both":[129],"cases":[133],"these":[135],"systems,":[138],"which":[139],"an":[141],"added":[142],"advantage":[143],"algorithm.":[146]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}