{"id":"https://openalex.org/W4413132820","doi":"https://doi.org/10.1137/23m1563967","title":"Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs","display_name":"Modeling Still Matters: A Surprising Instance of Catastrophic Floating Point Errors in Mathematical Biology and Numerical Methods for ODEs","publication_year":2025,"publication_date":"2025-08-07","ids":{"openalex":"https://openalex.org/W4413132820","doi":"https://doi.org/10.1137/23m1563967"},"language":"en","primary_location":{"id":"doi:10.1137/23m1563967","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1563967","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","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/A5041188954","display_name":"Cordula Reisch","orcid":"https://orcid.org/0000-0003-1442-1474"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Cordula Reisch","raw_affiliation_strings":["Institut for Partial Differential Equations, TU Braunschweig, Braunschweig, 38106 Germany"],"raw_orcid":"https://orcid.org/0000-0003-1442-1474","affiliations":[{"raw_affiliation_string":"Institut for Partial Differential Equations, TU Braunschweig, Braunschweig, 38106 Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056123559","display_name":"Hendrik Ranocha","orcid":"https://orcid.org/0000-0002-3456-2277"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hendrik Ranocha","raw_affiliation_strings":["Applied Mathematics, University of Hamburg, Hamburg, Germany. Current address: Institute of Mathematics, Johannes Gutenberg University Mainz, Mainz, 55128 Germany"],"raw_orcid":"https://orcid.org/0000-0002-3456-2277","affiliations":[{"raw_affiliation_string":"Applied Mathematics, University of Hamburg, Hamburg, Germany. Current address: Institute of Mathematics, Johannes Gutenberg University Mainz, Mainz, 55128 Germany","institution_ids":["https://openalex.org/I159176309","https://openalex.org/I197323543"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.25593926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"67","issue":"3","first_page":"624","last_page":"641"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9857000112533569,"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/T13286","display_name":"Modeling and Simulation Systems","score":0.9472000002861023,"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/ode","display_name":"Ode","score":0.7944961786270142},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.7162207365036011},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.634171724319458},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.631514847278595},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5586254000663757},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5548379421234131},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5279946327209473},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.46759742498397827},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44637733697891235},{"id":"https://openalex.org/keywords/computer-simulation","display_name":"Computer simulation","score":0.4447783827781677},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.42135581374168396},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4152102768421173},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.41229259967803955},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2523000240325928},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.2301149070262909},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1641877293586731},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.14996996521949768},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1339748203754425},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09522536396980286},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08403375744819641}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7944961786270142},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.7162207365036011},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.634171724319458},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.631514847278595},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5586254000663757},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5548379421234131},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5279946327209473},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.46759742498397827},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44637733697891235},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.4447783827781677},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.42135581374168396},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4152102768421173},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.41229259967803955},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2523000240325928},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.2301149070262909},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1641877293586731},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.14996996521949768},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1339748203754425},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09522536396980286},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08403375744819641},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1563967","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1563967","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.8700000047683716}],"awards":[{"id":"https://openalex.org/G1244266449","display_name":null,"funder_award_id":"32\u201010/22","funder_id":"https://openalex.org/F4320321626","funder_display_name":"Daimler und Benz Stiftung"},{"id":"https://openalex.org/G2580521021","display_name":"Effiziente, strukturerhaltende Verfahren hoher Ordnung f\u00fcr nichtlineare Evolutionsgleichungen","funder_award_id":"513301895","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321626","display_name":"Daimler und Benz Stiftung","ror":"https://ror.org/046pf6524"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1965307823","https://openalex.org/W1982955378","https://openalex.org/W2008856901","https://openalex.org/W2035695789","https://openalex.org/W2059625173","https://openalex.org/W2072226973","https://openalex.org/W2081518023","https://openalex.org/W2084367325","https://openalex.org/W2116055501","https://openalex.org/W2117453669","https://openalex.org/W2120575449","https://openalex.org/W2144144709","https://openalex.org/W2619381903","https://openalex.org/W2808029806","https://openalex.org/W2945076242","https://openalex.org/W2963129791","https://openalex.org/W2964044368","https://openalex.org/W3011239099","https://openalex.org/W3037352865","https://openalex.org/W3134568949","https://openalex.org/W3164758163","https://openalex.org/W4214727197","https://openalex.org/W4283392959","https://openalex.org/W4284886798","https://openalex.org/W4292994524","https://openalex.org/W4295124794","https://openalex.org/W4386792185"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2958348684","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W3178131028","https://openalex.org/W47811045","https://openalex.org/W2243194968"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,55,111],"guide":[2],"the":[3,15,57,64,68,72,91,104,124],"reader":[4],"on":[5],"a":[6,39],"journey":[7],"through":[8],"mathematical":[9,42],"modeling":[10],"and":[11,30,70,96,136],"numerical":[12,31,45,83,97,125],"analysis,":[13],"emphasizing":[14],"crucial":[16],"interplay":[17],"of":[18,27,67,74,93],"both":[19],"disciplines.":[20],"Targeting":[21],"undergraduate":[22],"students":[23],"with":[24,122],"basic":[25],"knowledge":[26,95],"dynamical":[28],"systems":[29],"methods":[32,46],"for":[33,59,82,138],"ordinary":[34],"differential":[35],"equations,":[36],"we":[37],"explore":[38],"model":[40,69,80],"from":[41],"biology":[43],"where":[44,103],"fail":[47],"badly":[48],"due":[49],"to":[50,76,89,130],"catastrophic":[51],"floating":[52],"point":[53],"errors.":[54],"analyze":[56],"reasons":[58],"this":[60,128,132],"behavior":[61],"by":[62],"studying":[63],"steady":[65],"states":[66],"use":[71],"theory":[73],"invariants":[75],"develop":[77],"an":[78,115,119],"alternative":[79],"suited":[81],"simulations.":[84],"Our":[85],"story":[86],"is":[87],"intended":[88],"motivate":[90],"combining":[92],"analytical":[94],"knowledge,":[98],"even":[99],"in":[100,127],"those":[101],"cases":[102],"world":[105],"looks":[106],"fine":[107],"at":[108],"first":[109],"sight.":[110],"have":[112],"set":[113],"up":[114],"online":[116],"repository":[117],"containing":[118],"interactive":[120],"notebook":[121],"all":[123],"experiments":[126],"article":[129],"make":[131],"study":[133],"fully":[134],"reproducible":[135],"useful":[137],"classroom":[139],"teaching.":[140]},"counts_by_year":[],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}