{"id":"https://openalex.org/W7167266274","doi":"https://doi.org/10.1007/s11075-026-02426-4","title":"General linear method with F-property and inherent quadratic stability for solving stiff differential systems","display_name":"General linear method with F-property and inherent quadratic stability for solving stiff differential systems","publication_year":2026,"publication_date":"2026-07-03","ids":{"openalex":"https://openalex.org/W7167266274","doi":"https://doi.org/10.1007/s11075-026-02426-4"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-026-02426-4","doi":"https://doi.org/10.1007/s11075-026-02426-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-026-02426-4","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.researchsquare.com/article/rs-8711138/latest.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064557664","display_name":"Sakshi Gautam","orcid":"https://orcid.org/0000-0002-2811-1859","observed_orcids":["https://orcid.org/0000-0002-2811-1859","https://orcid.org/0009-0007-3010-0853"]},"institutions":[{"id":"https://openalex.org/I8977528","display_name":"Dr. Hari Singh Gour University","ror":"https://ror.org/01xapxe37","country_code":"IN","type":"education","lineage":["https://openalex.org/I8977528"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sakshi Gautam","raw_affiliation_strings":["Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, (A Central University), Sagar, 470001, Madhya Pradesh, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, (A Central University), Sagar, 470001, Madhya Pradesh, India","institution_ids":["https://openalex.org/I8977528"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019234865","display_name":"Ram K. Pandey","orcid":"https://orcid.org/0000-0002-8176-8729","observed_orcids":["https://orcid.org/0000-0002-8176-8729"]},"institutions":[{"id":"https://openalex.org/I8977528","display_name":"Dr. Hari Singh Gour University","ror":"https://ror.org/01xapxe37","country_code":"IN","type":"education","lineage":["https://openalex.org/I8977528"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ram K. Pandey","raw_affiliation_strings":["Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, (A Central University), Sagar, 470001, Madhya Pradesh, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, (A Central University), Sagar, 470001, Madhya Pradesh, India","institution_ids":["https://openalex.org/I8977528"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064557664"],"corresponding_institution_ids":["https://openalex.org/I8977528"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.51773511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.00019999999494757503,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":9.999999747378752e-05,"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/general-linear-methods","display_name":"general linear methods","score":1.0},{"id":"https://openalex.org/keywords/runge-kutta-methods","display_name":"Runge-Kutta method","score":0.6589999794960022},{"id":"https://openalex.org/keywords/matrix-equivalence","display_name":"matrix equivalence","score":0.7419999837875366}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7638000249862671},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5479999780654907},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5202000141143799},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5149000287055969},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5042999982833862},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4832000136375427},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4717000126838684},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.45890000462532043},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4350000023841858},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4212000072002411},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.37940001487731934},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.35760000348091125},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.3109999895095825},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.2540999948978424},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2524999976158142},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.2513999938964844},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11075-026-02426-4","doi":"https://doi.org/10.1007/s11075-026-02426-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-026-02426-4","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"doi:10.21203/rs.3.rs-8711138/v1","doi":"https://doi.org/10.21203/rs.3.rs-8711138/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-8711138/v1","pdf_url":"https://www.researchsquare.com/article/rs-8711138/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.21203/rs.3.rs-8711138/v1","doi":"https://doi.org/10.21203/rs.3.rs-8711138/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-8711138/v1","pdf_url":"https://www.researchsquare.com/article/rs-8711138/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7167266274.pdf","grobid_xml":"https://content.openalex.org/works/W7167266274.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1543750907","https://openalex.org/W1557080381","https://openalex.org/W1633806305","https://openalex.org/W1902819800","https://openalex.org/W1970066377","https://openalex.org/W1995504856","https://openalex.org/W1996705524","https://openalex.org/W2003180820","https://openalex.org/W2033359289","https://openalex.org/W2039319854","https://openalex.org/W2050296550","https://openalex.org/W2053096573","https://openalex.org/W2060608186","https://openalex.org/W2060988134","https://openalex.org/W2084263447","https://openalex.org/W2091967202","https://openalex.org/W2093045686","https://openalex.org/W2096763158","https://openalex.org/W2144144709","https://openalex.org/W2152265807","https://openalex.org/W2480201659","https://openalex.org/W2734861480","https://openalex.org/W2809790425","https://openalex.org/W3000320365","https://openalex.org/W4400424154","https://openalex.org/W4406037585"],"related_works":["https://openalex.org/W4417142607","https://openalex.org/W2033359289","https://openalex.org/W2306576164","https://openalex.org/W2138301603","https://openalex.org/W4403335677","https://openalex.org/W2577664770","https://openalex.org/W7096985269","https://openalex.org/W2553034758","https://openalex.org/W2508756916","https://openalex.org/W1633806305"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"work":[2,171],"introduces":[3],"a":[4,48,110,152],"new":[5],"class":[6],"of":[7,15,51,73,93,124,140,165],"general":[8],"linear":[9],"methods":[10,32,68],"(GLMs)":[11],"for":[12,86,102,118,146],"solving":[13],"systems":[14,89],"time-dependent":[16],"differential":[17,88,95],"equations,":[18],"based":[19],"on":[20,133],"the":[21,28,45,55,70,80,114,122,125,141,148,156],"Nordsieck":[22],"input":[23],"vector":[24],"and":[25,37,62,170],"equipped":[26],"with":[27,44,54,69,79,109,155],"\\emph{F}-property.":[29,126],"The":[30,98,127,138,159],"proposed":[31,128],"are":[33,83,130,161],"characterized":[34],"by":[35],"$r=s=p+1$":[36],"satisfy":[38],"inherent":[39],"quadratic":[40],"stability":[41],"criteria.":[42],"GLMs":[43,78],"\\emph{F}-property":[46,81],"offer":[47],"natural":[49],"extension":[50],"Runge\u2013Kutta":[52],"schemes":[53,105],"\\emph{first":[56],"same":[57,71],"as":[58],"last}":[59],"(FSAL)":[60],"property":[61],"provide":[63],"improved":[64],"efficiency":[65],"over":[66],"non-FSAL":[67],"number":[72],"stages.":[74],"We":[75],"develop":[76],"implicit":[77],"that":[82],"well":[84],"suited":[85],"stiff":[87],"arising":[90],"from":[91],"semi-discretization":[92],"partial":[94],"equations":[96],"(PDEs).":[97],"theoretical":[99],"framework":[100],"needed":[101],"constructing":[103],"these":[104],"is":[106],"presented,":[107],"along":[108],"key":[111],"modification":[112],"in":[113,121],"matrix":[115],"equivalence":[116],"necessary":[117],"enforcing":[119],"IQS":[120],"presence":[123],"classes":[129],"then":[131],"tested":[132],"three":[134,149],"different":[135],"test":[136],"problems.":[137],"results":[139,160],"numerical":[142],"simulations":[143],"carried":[144],"out":[145],"all":[147],"problems":[150],"reveal":[151],"good":[153],"agreement":[154],"reference":[157],"solutions.":[158],"interpreted":[162],"using":[163],"computation":[164],"error":[166],"norms,":[167],"estimated":[168],"orders,":[169],"precision":[172],"diagrams.":[173]},"counts_by_year":[],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2026-07-04T00:00:00"}