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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.
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