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USCD1229 LSODES

LSODES, Ordinary Differential Equations System Sparse Matrices

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1. NAME OR DESIGNATION OF PROGRAM:  LSODES.
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2. COMPUTERS
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Program name Package id Status Status date
LSODES USCD1229/01 Tested 23-SEP-2005

Machines used:

Package ID Orig. computer Test computer
USCD1229/01 IBM PC PC Windows
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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.
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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.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
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6. TYPICAL RUNNING TIME
USCD1229/01
At the NEA-DB the demonstration program included in this package ran on a PC Windows Xeon in a few seconds.
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7. UNUSUAL FEATURES
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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.
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9. STATUS
Package ID Status date Status
USCD1229/01 23-SEP-2005 Tested at NEADB
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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.
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11. HARDWARE REQUIREMENTS
USCD1229/01
Compiling, loading, and executing the demonstration program require a minimum main storage of 5 Mbytes.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
USCD1229/01 FORTRAN-77
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13. SOFTWARE REQUIREMENTS
USCD1229/01
DOS under Windows XP.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS
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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
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16. MATERIAL AVAILABLE
USCD1229/01
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
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: algorithms, initial-value problems, numerical solution, ordinary differential equations.