USCD1229 LSODES

1. NAME OR DESIGNATION OF PROGRAM:  LSODES.

3. DESCRIPTION OF PROGRAM OR FUNCTION

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. It then uses parts of the Yale Sparse Matrix Package (YSMP) to solve the linear systems that arise, by a sparse (direct) LU factorization/backsolve method. The LSODES source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available.

4. METHODS

It is assumed that the ODEs 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. LSODES is used for each of the relevant values of mf to solve the problem ydot = A * y, where A is the 9 by 9 sparse matrix

-4  1     1
                1 -4  1     1
                   1 -4        1
                        -4  1     1
       A =               1 -4  1     1
                            1 -4        1
                                 -4  1
                                  1 -4  1
                                     1 -4

The initial conditions are  y(0) = (1, 2, 3, ..., 9).
Output is printed at t = 1, 2, and 3.
Each case is solved first with nominal (large) values of lrw and liw, and then with values given by lenrw and leniw (optional outputs) on the first run, as a check on these computed work array lengths. If the errors are too large, or other difficulty occurs, a warning message is printed.

At the NEA-DB the demonstration program included in this package ran on a PC Windows Xeon in a few seconds.

8. RELATED OR AUXILIARY PROGRAMS

This program is part of the ODEPACK (USCD1232) collection of Fortran solvers for the initial value problem for ordinary differential equation systems.  It consists of nine solvers, namely a basic solver called LSODE (USCD1223) and eight variants of it: LSODES (USCD1229), LSODA (USCD1227), LSODAR (USCD1228), LSODPK (USCD1231), LSODKR (USCD1230), LSODI (USCD1224), LSOIBT (USCD1226), and LSODIS (USCD1225) which are distributed by the Computer Program Service of the NEA Data Bank.

10. REFERENCES

[1]  A. C. Hindmarsh, "ODEPACK, A Systematized Collection of ODE Solvers," in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.
[2]  P. N. Brown and A. C. Hindmarsh, "Reduced Storage Matrix Methods in Stiff ODE Systems," J. Appl. Math. & Comp., 31 (1989), pp.40-91. 11.

Compiling, loading, and executing the demonstration program require a minimum main storage of 5 Mbytes.

DOS under Windows XP.

15. NAME AND ESTABLISHMENT OF AUTHORS

A.C. Hindmarsh* and L. R. Petzold
Lawrence Livermore National Laboratory
P.O. Box 808
Livermore, California 94550,
USA
* Contact

Information file
Double precision files:
DLSODES_MAIN.exe Executable file
DLSODES_MAIN.f Test Source file
DLSODES_OUT.aut Author's output file
DLSODES_OUT.nea NEA output file
opkda1.f  Fortran source file
opkda2.f  Fortran source file
opkdmain.f  Fortran source file
Single precision files
opksa1.f  Fortran source file
opksa2.f Fortran source file
opksmain.f  Fortran source file
SLSODES_MAIN.exe Executable file
SLSODES_MAIN.f Test source file
SLSODES_OUT.nea NEA output file