{"id":"https://openalex.org/W7130432123","doi":"https://doi.org/10.48550/arxiv.2602.15271","title":"A Patankar predictor-corrector approach for positivity-preserving time integration","display_name":"A Patankar predictor-corrector approach for positivity-preserving time integration","publication_year":2026,"publication_date":"2026-02-17","ids":{"openalex":"https://openalex.org/W7130432123","doi":"https://doi.org/10.48550/arxiv.2602.15271"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.15271","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15271","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.15271","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126349733","display_name":"Kamila Nurkhametova","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nurkhametova, Kamila","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010904702","display_name":"Reid J. Gomillion","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gomillion, Reid J.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126359769","display_name":"Amit N. Subrahmanya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Subrahmanya, Amit N.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126333478","display_name":"Adrian Sandu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sandu, Adrian","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5126349733"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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":0.9840999841690063,"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":0.9840999841690063,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.004600000102072954,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.002400000113993883,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/integrator","display_name":"Integrator","score":0.6078000068664551},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.569599986076355},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5077000260353088},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.4921000003814697},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.45910000801086426},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.44589999318122864},{"id":"https://openalex.org/keywords/clipping","display_name":"Clipping (morphology)","score":0.44200000166893005},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.428600013256073}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6866999864578247},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.6078000068664551},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.569599986076355},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5077000260353088},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4968000054359436},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.4921000003814697},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.45910000801086426},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.44589999318122864},{"id":"https://openalex.org/C2776848632","wikidata":"https://www.wikidata.org/wiki/Q853463","display_name":"Clipping (morphology)","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.428600013256073},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.41749998927116394},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.4004000127315521},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3262999951839447},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2872999906539917},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.2797999978065491},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2768000066280365},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.15271","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15271","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.15271","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15271","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.6624239087104797,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Many":[0],"natural":[1],"processes,":[2],"such":[3],"as":[4,12],"chemical":[5],"reactions":[6],"and":[7,19,30,69,86,109,125,180],"wave":[8],"dynamics,":[9],"are":[10,140],"modeled":[11],"production-destruction":[13],"(PD)":[14],"systems":[15,104],"that":[16,45,66,118,173],"obey":[17],"positivity":[18,29,124,163],"linear":[20],"conservation":[21],"laws.":[22],"Classical":[23],"time":[24],"integrators":[25,186],"do":[26],"not":[27],"guarantee":[28],"can":[31,46],"produce":[32],"negative":[33],"or":[34],"nonphysical":[35],"numerical":[36],"solutions.":[37,76],"This":[38],"paper":[39],"presents":[40],"a":[41,63,79,110,178],"modular":[42],"correction":[43,161],"strategy":[44,58],"be":[47],"applied":[48,134],"to":[49,72,94,136,167,183],"implicit":[50],"Runge-Kutta":[51,158],"schemes,":[52,159],"in":[53,142,153],"particular":[54],"SDIRK":[55,121],"methods.":[56],"The":[57],"combines":[59],"stage-wise":[60],"clipping":[61],"with":[62],"ratio-based":[64],"scaling":[65],"enforces":[67],"invariants":[68,126],"is":[70],"guaranteed":[71],"yield":[73],"nonnegative,":[74],"conservative":[75],"We":[77],"provide":[78],"theoretical":[80],"analysis":[81],"of":[82,91,130],"the":[83,95,119,137,160,174],"corrected":[84,120],"schemes":[85],"characterize":[87],"their":[88],"worst-case":[89],"order":[90],"accuracy":[92],"relative":[93],"underlying":[96],"base":[97],"method.":[98],"Numerical":[99],"experiments":[100],"on":[101],"stiff":[102,188],"ODE":[103],"(Robertson,":[105],"MAPK,":[106],"stratospheric":[107],"chemistry)":[108],"nonlinear":[111],"PDE":[112],"(the":[113],"Korteweg-De":[114],"Vries":[115],"equation)":[116],"demonstrate":[117],"methods":[122],"preserve":[123],"without":[127],"significant":[128],"loss":[129],"accuracy.":[131],"Importantly,":[132],"corrections":[133],"only":[135],"final":[138],"stage":[139],"sufficient":[141],"practice,":[143],"while":[144],"applying":[145],"them":[146],"at":[147],"all":[148],"stages":[149],"may":[150],"distort":[151],"dynamics":[152],"some":[154],"cases.":[155],"For":[156],"explicit":[157],"maintained":[162],"but":[164],"reduced":[165],"convergence":[166],"first":[168],"order.":[169],"These":[170],"results":[171],"show":[172],"proposed":[175],"framework":[176],"provides":[177],"simple":[179],"effective":[181],"way":[182],"construct":[184],"positivity-preserving":[185],"for":[187],"PD":[189],"systems.":[190]},"counts_by_year":[],"updated_date":"2026-02-19T06:31:58.851227","created_date":"2026-02-19T00:00:00"}