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However, solving such equations can be prohibitively expensive, easily taxing the world\u2019s largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger \u201couter-loop\u201d time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale Computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently. <\/jats:p>","DOI":"10.1177\/10943420241280060","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T16:49:39Z","timestamp":1728060579000},"page":"123-146","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["SUNDIALS time integrators for exascale applications with many independent systems of ordinary differential equations"],"prefix":"10.1177","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9138-0720","authenticated-orcid":false,"given":"Cody J","family":"Balos","sequence":"first","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA"}]},{"given":"Marcus","family":"Day","sequence":"additional","affiliation":[{"name":"Computational Science Center, National Renewable Energy Laboratory, Golden, CO, USA"}]},{"given":"Lucas","family":"Esclapez","sequence":"additional","affiliation":[{"name":"Computational Science Center, National Renewable Energy Laboratory, Golden, CO, USA"}]},{"given":"Anne M","family":"Felden","sequence":"additional","affiliation":[{"name":"Process and Energy Department, Delft University of Technology, Delft, The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7993-8282","authenticated-orcid":false,"given":"David J","family":"Gardner","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA"}]},{"given":"Malik","family":"Hassanaly","sequence":"additional","affiliation":[{"name":"Computational Science Center, National Renewable Energy Laboratory, Golden, CO, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0911-7841","authenticated-orcid":false,"given":"Daniel R","family":"Reynolds","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Southern Methodist University, Dallas, TX, USA"}]},{"given":"Jon S","family":"Rood","sequence":"additional","affiliation":[{"name":"Computational Science Center, National Renewable Energy Laboratory, Golden, CO, USA"}]},{"given":"Jean M","family":"Sexton","sequence":"additional","affiliation":[{"name":"Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA, USA"}]},{"given":"Nicholas T","family":"Wimer","sequence":"additional","affiliation":[{"name":"Computational Science Center, National Renewable Energy Laboratory, Golden, CO, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6502-8659","authenticated-orcid":false,"given":"Carol S","family":"Woodward","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA"}]}],"member":"179","published-online":{"date-parts":[[2024,10,4]]},"reference":[{"key":"bibr1-10943420241280060","doi-asserted-by":"publisher","DOI":"10.1109\/ScalA54577.2021.00010"},{"key":"bibr2-10943420241280060","doi-asserted-by":"publisher","DOI":"10.1088\/0004-637X\/765\/1\/39"},{"key":"bibr3-10943420241280060","doi-asserted-by":"publisher","DOI":"10.1145\/3480935"},{"key":"bibr4-10943420241280060","doi-asserted-by":"publisher","DOI":"10.1016\/j.parco.2021.102836"},{"key":"bibr5-10943420241280060","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stac3294"},{"key":"bibr6-10943420241280060","doi-asserted-by":"crossref","unstructured":"Chabanier S, Ravoux C, Latrille L, et al. 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