Here's what is available (all in double precision):
LSODE
LSODES
LSODA
LSODAR
LSODI
LSOIBT

To receive the document try:
send only DOC from odepack

To receive the demo program try:
send only DEMO from odepack



                     I. Summary of the ODEPACK Solvers


  A. Solvers for explicitly given systems.

       In the solvers below, it is assumed that the ODE's are given
  explicitly, so that the system can be written in the form
          dy/dt  =  f(t,y) ,
  where y is the vector of dependent variables, and t is the independent
  variable.


  1. LSODE (Livermore Solver for Ordinary Differential Equations) is the
     basic solver of the collection.  It solves stiff and nonstiff systems
     of the form dy/dt = f.  In the stiff case, it treats the Jacobian matrix
     df/dy as either a full or a banded matrix, and as either user-supplied
     or internally approximated by difference quotients.  It uses Adams methods
     (predictor-corrector) in the nonstiff case, and Backward Differentiation
     Formula (BDF) methods in the stiff case.  The linear systems that arise
     are solved by direct methods (LU factor/solve).  LSODE supersedes the older
     GEAR and GEARB packages, and reflects a complete redesign of the user
     interface and internal organization, with some algorithmic improvements.


  2. LSODES, written jointly with A. H. Sherman, solves systems dy/dt = f
     and in the stiff case treats the Jacobian matrix in general sparse
     form.  It determines the sparsity structure on its own (or optionally
     accepts this information from the user), and uses parts of the Yale Sparse
     Matrix Package (YSMP) to solve the linear systems that arise.
     LSODES supersedes, and improves upon, the older GEARS package.


  3. LSODA, written jointly with L. R. Petzold, solves systems dy/dt = f
     with a full or banded Jacobian when the problem is stiff, but it
     automatically selects between nonstiff (Adams) and stiff (BDF) methods.
     It uses the nonstiff method initially, and dynamically monitors data
     in order to decide which method to use.


  4. LSODAR, also written jointly with L. R. Petzold, is a variant of LSODA
     with a rootfinding capability added.  Thus it solves problems dy/dt = f
     with full or banded Jacobian and automatic method selection, and at
     the same time, it finds the roots of any of a set of given functions
     of the form g(t,y).  This is often useful for finding stop conditions
     or points at which switches are to be made in the function f.


  B. Solvers for linearly implicit systems.

       In the solvers below, it is assumed that the derivative dy/dt is
  implicit, but occurs linearly, so that the system can be written
          A(t,y) dy/dt  =  g(t,y) ,
  where A is a square matrix.  These solvers allow A to be singular,
  in which case the system is a differential-algebraic system, but in that
  case users must be very careful to supply a well-posed problem with
  consistent initial conditions.


  5. LSODI, written jointly with J. F. Painter, solves linearly implicit
     systems in which the matrices involved (A, dg/dy, and d(A dy/dt)/dy) are
     all assumed to be either full or banded.  LSODI supersedes the older
     GEARIB solver and improves upon it in numerous ways.


  6. LSOIBT, written jointly with C. S. Kenney, solves linearly implicit
     systems in which the matrices involved are all assumed to be
     block-tridiagonal.  Linear systems are solved by the LU method.