{"id":"https://openalex.org/W4408798499","doi":"https://doi.org/10.3390/axioms14040245","title":"On High-Order Runge\u2013Kutta Pairs for Linear Inhomogeneous Problems","display_name":"On High-Order Runge\u2013Kutta Pairs for Linear Inhomogeneous Problems","publication_year":2025,"publication_date":"2025-03-24","ids":{"openalex":"https://openalex.org/W4408798499","doi":"https://doi.org/10.3390/axioms14040245"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14040245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040245","pdf_url":"https://www.mdpi.com/2075-1680/14/4/245/pdf?version=1742811019","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/4/245/pdf?version=1742811019","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042145292","display_name":"Houssem Jerbi","orcid":"https://orcid.org/0000-0003-1816-3767"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Houssem Jerbi","raw_affiliation_strings":["Department of Industrial Engineering, College of Engineering, University of Ha\u2019il, Hail 81481, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1816-3767","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, College of Engineering, University of Ha\u2019il, Hail 81481, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115846118","display_name":"Sanaa Maali","orcid":null},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Sanaa Maali","raw_affiliation_strings":["Department of Computer Science, Applied College, University of Ha\u2019il, Hail 81481, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Applied College, University of Ha\u2019il, Hail 81481, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038425434","display_name":"Sondess Ben Aoun","orcid":"https://orcid.org/0000-0003-2100-330X"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Sondess Ben Aoun","raw_affiliation_strings":["Department of Computer Engineering, College of Computer Science and Engineering, University of Ha\u2019il, Hail 81481, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, College of Computer Science and Engineering, University of Ha\u2019il, Hail 81481, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5097194856","display_name":"Arwa N. Aledaily","orcid":null},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Arwa N. Aledaily","raw_affiliation_strings":["Department of Information and Computer Science, College of Computer Science and Engineering, University of Ha\u2019il, Hail 81481, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Science, College of Computer Science and Engineering, University of Ha\u2019il, Hail 81481, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116778066","display_name":"Vijipriya Jeyamani","orcid":"https://orcid.org/0000-0003-0026-2636"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Vijipriya Jeyamani","raw_affiliation_strings":["Department of Computer Engineering, College of Computer Science and Engineering, University of Ha\u2019il, Hail 81481, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-0026-2636","affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, College of Computer Science and Engineering, University of Ha\u2019il, Hail 81481, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081822197","display_name":"Theodore E. Simos","orcid":"https://orcid.org/0000-0002-9220-6924"},"institutions":[{"id":"https://openalex.org/I147962203","display_name":"Democritus University of Thrace","ror":"https://ror.org/03bfqnx40","country_code":"GR","type":"education","lineage":["https://openalex.org/I147962203"]},{"id":"https://openalex.org/I179311214","display_name":"Gulf University for Science & Technology","ror":"https://ror.org/04d9rzd67","country_code":"KW","type":"education","lineage":["https://openalex.org/I179311214"]},{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN","GR","KW"],"is_corresponding":true,"raw_author_name":"Theodore E. Simos","raw_affiliation_strings":["Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref, Kuwait City 32093, Kuwait","School of Mechanical Engineering, Hangzhou Dianzi University, Er Hao Da Jie 1158, Xiasha, Hangzhou 310018, China","Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece"],"raw_orcid":"https://orcid.org/0000-0002-9220-6924","affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref, Kuwait City 32093, Kuwait","institution_ids":["https://openalex.org/I179311214"]},{"raw_affiliation_string":"School of Mechanical Engineering, Hangzhou Dianzi University, Er Hao Da Jie 1158, Xiasha, Hangzhou 310018, China","institution_ids":["https://openalex.org/I50760025"]},{"raw_affiliation_string":"Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece","institution_ids":["https://openalex.org/I147962203"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006207605","display_name":"Ch. Tsitouras","orcid":"https://orcid.org/0000-0001-6801-8117"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Charalampos Tsitouras","raw_affiliation_strings":["General Department, National & Kapodistrian University of Athens, GR34-400 Euripus Campus, 34400 Psachna, Greece"],"raw_orcid":"https://orcid.org/0000-0001-6801-8117","affiliations":[{"raw_affiliation_string":"General Department, National & Kapodistrian University of Athens, GR34-400 Euripus Campus, 34400 Psachna, Greece","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5081822197"],"corresponding_institution_ids":["https://openalex.org/I147962203","https://openalex.org/I179311214","https://openalex.org/I50760025"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":5.8076,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.95190252,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"245","last_page":"245"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976000189781189,"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/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.6776625514030457},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6376028060913086},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5171279311180115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.405878484249115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3729284107685089},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25096386671066284},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.11074411869049072},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1105896532535553}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.6776625514030457},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6376028060913086},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5171279311180115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.405878484249115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3729284107685089},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25096386671066284},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.11074411869049072},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1105896532535553},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14040245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040245","pdf_url":"https://www.mdpi.com/2075-1680/14/4/245/pdf?version=1742811019","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:135e84ca6bdc4dc78b6e06af51307435","is_oa":true,"landing_page_url":"https://doaj.org/article/135e84ca6bdc4dc78b6e06af51307435","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 4, p 245 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14040245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040245","pdf_url":"https://www.mdpi.com/2075-1680/14/4/245/pdf?version=1742811019","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408798499.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1595159159","https://openalex.org/W1989955731","https://openalex.org/W1995438682","https://openalex.org/W2005137148","https://openalex.org/W2010379067","https://openalex.org/W2022310475","https://openalex.org/W2027413093","https://openalex.org/W2040679101","https://openalex.org/W2040798430","https://openalex.org/W2054836446","https://openalex.org/W2081518023","https://openalex.org/W2132260313","https://openalex.org/W3044392373","https://openalex.org/W3209416867","https://openalex.org/W4210871879","https://openalex.org/W4367664734","https://openalex.org/W4378420955"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W4206768127","https://openalex.org/W1979597421","https://openalex.org/W4213270568","https://openalex.org/W2007980826","https://openalex.org/W4301315183","https://openalex.org/W2157764110","https://openalex.org/W2061531152"],"abstract_inverted_index":{"This":[0,190],"paper":[1],"introduces":[2],"a":[3,33,56,89,120,174,183],"novel":[4],"Runge\u2013Kutta":[5],"(RK)":[6],"pair":[7],"of":[8,40,59,78,98,125,151,197],"orders":[9,41],"8(6)":[10],"designed":[11],"specifically":[12],"for":[13,141,177,201],"solving":[14,178],"linear":[15,64,114,179],"inhomogeneous":[16,65,180],"initial":[17],"value":[18],"problems":[19,142],"(IVPs)":[20],"with":[21,156,211],"constant":[22],"coefficients.":[23],"The":[24,48,100,130,149,167],"proposed":[25],"method":[26,153],"requires":[27],"only":[28],"11":[29],"stages":[30,51],"per":[31],"iteration,":[32],"significant":[34],"improvement":[35],"over":[36,146],"conventional":[37],"RK":[38,102],"pairs":[39],"8(7),":[42],"which":[43],"typically":[44],"demand":[45],"13":[46],"stages.":[47],"reduction":[49],"in":[50,123,162,205],"is":[52,106],"achieved":[53],"by":[54],"leveraging":[55],"smaller":[57],"set":[58],"order":[60],"conditions":[61],"tailored":[62],"to":[63,93,193],"problems,":[66,111],"where":[67,207],"traditional":[68,208],"simplification":[69],"techniques":[70],"are":[71,154],"not":[72],"applicable.":[73],"To":[74],"address":[75],"the":[76,82,85,95,152,170,194],"complexity":[77],"deriving":[79],"such":[80],"methods,":[81],"authors":[83],"employ":[84],"Differential":[86],"Evolution":[87],"algorithm,":[88],"global":[90],"optimization":[91],"technique,":[92],"solve":[94],"resulting":[96],"system":[97],"equations.":[99],"new":[101],"pair,":[103],"named":[104],"NEW8(6)Lin,":[105],"tested":[107],"on":[108],"several":[109],"benchmark":[110],"including":[112],"scalar,":[113],"inhomogeneous,":[115],"and":[116,127,135,188],"larger":[117],"systems,":[118],"demonstrating":[119],"superior":[121],"performance":[122],"terms":[124],"accuracy":[126,134],"computational":[128,163,186],"efficiency.":[129],"method\u2019s":[131,171],"high":[132,144,157],"phase-lag":[133],"efficiency":[136,212],"make":[137],"it":[138],"particularly":[139,204],"suitable":[140],"requiring":[143],"precision":[145],"extended":[147],"intervals.":[148],"coefficients":[150],"provided":[155],"precision,":[158],"enabling":[159],"direct":[160],"implementation":[161],"environments":[164],"like":[165],"Mathematica.":[166],"results":[168],"highlight":[169],"potential":[172],"as":[173],"robust":[175],"tool":[176],"IVPs,":[181],"offering":[182],"balance":[184],"between":[185],"cost":[187],"accuracy.":[189],"work":[191],"contributes":[192],"ongoing":[195],"development":[196],"specialized":[198],"numerical":[199],"methods":[200],"differential":[202],"equations,":[203],"scenarios":[206],"approaches":[209],"struggle":[210],"or":[213],"stability.":[214]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-06-24T13:16:06.693445","created_date":"2025-10-10T00:00:00"}