Not yet reviewed by Pith; the record is open.

High-quality ordinary differential equation (ODE) solver libraries have a long history, going back to the 1970s. Over the past several years we have implemented, on top of the PETSc linear and nonlinear solver package, a new general-purpose, extensive, extensible library for solving ODEs and differential algebraic equations (DAEs). Package includes support for both forward and adjoint sensitivities that can be easily utilized by the TAO optimization package, which is also part of PETSc. The ODE/DAE integrator library strives to be highly scalable but also to deliver high efficiency for modest-sized problems. The library includes explicit solvers, implicit solvers, and a collection of implicit-explicit solvers, all with a common user interface and runtime selection of solver types, adaptive error control, and monitoring of solution progress. The library also offers enormous flexibility in selection of nonlinear and linear solvers, including the entire suite of PETSc iterative solvers, as well as several parallel direct solvers.