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USCD1223 LSODE.

LSODE, 1st Order Stiff or Non-Stiff Ordinary Differential Equations System Initial Value Problems

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1. NAME OR DESIGNATION OF PROGRAM

LSODE.

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2. COMPUTERS
To submit a request, click below on the link of the version you wish to order. Only liaison officers are authorised to submit online requests. Rules for requesters are available here.
Program name Package id Status Status date
LSODE USCD1223/01 Tested 23-SEP-2005

Machines used:

Package ID Orig. computer Test computer
USCD1223/01 IBM PC PC Windows
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3. DESCRIPTION OF PROGRAM OR FUNCTION

LSODE (Livermore Solver for Ordinary Differential Equations) 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 dense (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 (the Gear methods) in the stiff case.  The linear systems that arise are solved by direct methods (LU factor/solve). The LSODE 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. LSODE contains two variable-order, variable- step (with interpolatory step-changing) integration methods. The first is the implicit Adams or nonstiff method, of orders one through twelve. The second is the backward differentiation or stiff method (or BDF method, or Gear's method), of orders one through five.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The differential equations must be given in explicit form, i.e., dy/dt = f(y,t). Problems with intermittent high-speed transients may cause inefficient or unstable performance.

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6. TYPICAL RUNNING TIME
USCD1223/01
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 OF THE PROGRAM

LSODE offers a great deal of flexibility as to choice of basic method, either stiff or nonstiff, nonlinear corrector iteration method - 6 choices, error tolerances including componentwise relative and absolute tolerances, stopping criterion - at a specified time, t, or after every step, possibly with a critical t, optional input controls, e.g. maximum order or print flags, optional output controls, e.g. step and function evaluation counts and derivatives of the solution, interrupt and restart capabilities, etc. Work space arrays and the names of the user-supplied routines are passed as subroutine arguments for flexibility. User-controlled dynamic work space, real and integer, can also be passed to the user routines.

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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
USCD1223/01 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.

  3. K. Radhakrishnan and A. C. Hindmarsh, "Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations," LLNL report UCRL-ID-113855, December 1993.

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11. HARDWARE REQUIREMENTS
USCD1223/01
Compiling, loading, and executing the demonstration program required a minimum main storage of 5 Mbytes.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
USCD1223/01 FORTRAN-77
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13. SOFTWARE REQUIREMENTS
USCD1223/01
DOS under Windows XP.
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15. NAME AND ESTABLISHMENT OF AUTHORS

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
USCD1223/01
Information file
Double precision files:
DLSODE_MAIN.exe Executable file
DLSODE_MAIN.f Test Source file
DLSODE_OUT.aut Author's output file
DLSODE_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
SLSODE_MAIN.exe Executable file
SLSODE_MAIN.f Test source file
SLSODE_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.