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The basic versions of these codes are called KINSOL, CVODE, and IDA, respectively. The codes are written in ANSI standard C and are suitable for either serial or parallel machine environments. Common and notable features of these codes include inexact Newton-Krylov methods for solving large-scale nonlinear systems; linear multistep methods for time-dependent problems; a highly modular structure to allow incorporation of different preconditioning and\/or linear solver methods; and clear interfaces allowing for users to provide their own data structures underneath the solvers. We describe the current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness. We also describe how the codes stem from previous and widely used Fortran 77 solvers, and how the codes have been augmented with forward and adjoint methods for carrying out first-order sensitivity analysis with respect to model parameters or initial conditions.<\/jats:p>","DOI":"10.1145\/1089014.1089020","type":"journal-article","created":{"date-parts":[[2005,11,7]],"date-time":"2005-11-07T16:00:45Z","timestamp":1131379245000},"page":"363-396","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2245,"title":["SUNDIALS"],"prefix":"10.1145","volume":"31","author":[{"given":"Alan C.","family":"Hindmarsh","sequence":"first","affiliation":[{"name":"Lawrence Livermore National Laboratory, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter N.","family":"Brown","sequence":"additional","affiliation":[{"name":"Lawrence Livermore National Laboratory, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Keith E.","family":"Grant","sequence":"additional","affiliation":[{"name":"Lawrence Livermore National Laboratory, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steven L.","family":"Lee","sequence":"additional","affiliation":[{"name":"Lawrence Livermore National Laboratory, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Radu","family":"Serban","sequence":"additional","affiliation":[{"name":"Lawrence Livermore National Laboratory, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dan E.","family":"Shumaker","sequence":"additional","affiliation":[{"name":"Lawrence Livermore National Laboratory, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carol S.","family":"Woodward","sequence":"additional","affiliation":[{"name":"Lawrence Livermore National Laboratory, Livermore, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2005,9]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"Brenan K. E. Campbell S. L. and Petzold L. R. 1996. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM Press Philadelphia PA.  Brenan K. E. Campbell S. L. and Petzold L. R. 1996. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM Press Philadelphia PA.","DOI":"10.1137\/1.9781611971224"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/0724031"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/0910062"},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/0096-3003(89)90110-0","article-title":"Reduced storage matrix methods in stiff ODE systems","volume":"31","author":"Brown P. N.","year":"1989","unstructured":"Brown , P. N. and Hindmarsh , A. C. 1989 . Reduced storage matrix methods in stiff ODE systems . J. Appl. Math. Comp. 31 , 49 -- 91 . Brown, P. N. and Hindmarsh, A. C. 1989. Reduced storage matrix methods in stiff ODE systems. J. Appl. Math. 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