Original post is here: eklausmeier.goip.de
Lawrence Livermore National Laboratory provides a suite of software packages for the solution of ordinary differential equations. This suite is called SUNDIALS.
SUNDIALS consists of
- CVODE: solves initial value problems for ordinary differential equation (ODE) systems; successor of GEAR, EPISODE, then LSODE
- CVODES: solves ODE systems and includes sensitivity analysis capabilities (forward and adjoint); successor of LSODES
- IDA: solves initial value problems for differential-algebraic equation (DAE) systems; successor of DASSL
- IDAS: solves DAE systems and includes sensitivity analysis capabilities (forward and adjoint); successor of DASSL
- KINSOL: solves nonlinear algebraic systems
These subroutines are all written in C and have separate Fortran interfaces. Its authors are Carol Woodward, Alan Hindmarsh, and Radu Serban. Others have also contributed to these codes.
An overview can be found in this presentation.
Various questions can be asked and searched here: sundials-users.
For decades LSODE was used as a yardstick for the numerical solution of ODEs.
More on the history of LSODE can be found in an interview with Alan Hindmarsh.
The source code is on GitHub.