{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:23:33Z","timestamp":1787333013575,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-22-1-0004"],"award-info":[{"award-number":["FA9550-22-1-0004"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2231482"],"award-info":[{"award-number":["DMS-2231482"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2025,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This work analyzes the sensitivities of the solution of a system of ordinary differential equations (ODEs) and a corresponding quantity of interest (QoI) to perturbations in a state-dependent component function that appears in the governing ODEs. This extends existing ODE sensitivity results, which consider the sensitivity of the ODE solution with respect to state-independent parameters. It is shown that with Carath\u00e9odory-type assumptions on the ODEs, the implicit function theorem can be applied to establish continuous Fr\u00e9chet differentiability of the ODE solution with respect to the component function. These sensitivities are used to develop new estimates for the change in the ODE solution or QoI when the component function is perturbed. In applications, this new sensitivity-based bound on the ODE solution or QoI error is often much tighter than classical Gronwall-type error bounds. The sensitivity-based error bounds are applied to a trajectory simulation for a hypersonic vehicle.<\/jats:p>","DOI":"10.1137\/25m1729563","type":"journal-article","created":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T07:49:57Z","timestamp":1759996197000},"page":"2094-2118","source":"Crossref","is-referenced-by-count":0,"title":["Sensitivity of ODE Solutions and Quantities of Interest with Respect to Component Functions in the Dynamics"],"prefix":"10.1137","volume":"63","author":[{"given":"Jonathan R.","family":"Cangelosi","sequence":"first","affiliation":[{"name":"Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-4035 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9305-4221","authenticated-orcid":true,"given":"Matthias","family":"Heinkenschloss","sequence":"additional","affiliation":[{"name":"Department of Computational Applied Mathematics and Operations Research, MS-134, Rice University, Houston, TX 77005-1892 USA, and the Ken Kennedy Institute, Rice University."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,10,9]]},"reference":[{"key":"ref1","series-title":"De Gruyter Studies in Mathematics 13","volume-title":"An Introduction to Nonlinear Analysis","author":"Amann H.","year":"1990"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511897450"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-2025-2_3"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718577"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/080729529"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.2514\/6.2024-0375"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7793-9"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1515\/9783110249996"},{"key":"ref9","series-title":"Springer Series in Computational Mathematics 8","author":"Hairer E.","year":"1993","edition":"2"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0015-5"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-5981-1"},{"key":"ref12","volume-title":"Applied Mathematical Sciences 124","author":"Polak E.","year":"1997"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-006-0069-9"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1108\/AEAT-04-2013-0079"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/112"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/120899042"},{"key":"ref17","series-title":"Applied Mathematical Sciences 109","volume-title":"Applied Functional Analysis: Main Principles and Their Applications","author":"Zeidler E.","year":"1995"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/25M1729563","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:25:40Z","timestamp":1787329540000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1729563"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,9]]},"references-count":17,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10,31]]}},"alternative-id":["10.1137\/25M1729563"],"URL":"https:\/\/doi.org\/10.1137\/25m1729563","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,9]]}}}