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USCD1224 LSODI.

LSODI, Implicit Ordinary Differential Equations System Either Dense or Banded Matrices

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1. NAME OR DESIGNATION OF PROGRAM:  LSODI.
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2. COMPUTERS
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Program name Package id Status Status date
LSODI USCD1224/01 Tested 23-SEP-2005

Machines used:

Package ID Orig. computer Test computer
USCD1224/01 IBM PC PC Windows
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3. DESCRIPTION OF PROGRAM OR FUNCTION

LSODI is a set of general-purpose FORTRAN routines solver for the initial value problem for ordinary differential equation systems. It is suitable for both stiff and nonstiff systems. LSODI treat systems in the linearly implicit form A(t,y) dy/dt = g(t,y), A = a square matrix, i.e. with the derivative dy/dt implicit, but linearly so. It allows A to be singular, in which case the system is a differential-algebraic equation (DAE) system.  In that case, the user must be very careful to supply a well-posed problem with consistent initial conditions. 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 dense or banded. The LSODI 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

This program solves a semi-discretized form of the Burgers equation,
     u  = -(u*u/2)  + eta * u
      t           x          xx
for a = -1 .le. x .le. 1 = b, t .ge. 0.
Here eta = 0.05.
Boundary conditions: u(-1,t) = u(1,t) = 0.
Initial profile: square wave
     u(0,x) = 0    for 1/2 .lt. abs(x) .le. 1
     u(0,x) = 1/2  for abs(x) = 1/2
     u(0,x) = 1    for 0 .le. abs(x) .lt. 1/2
An ODE system is generated by a simplified Galerkin treatment of the spatial variable x.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
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6. TYPICAL RUNNING TIME
USCD1224/01
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
USCD1224/01 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]  R. C. Y. Chin, G. W. Hedstrom, and K. E. Karlsson, "A Simplified Galerkin Method for Hyperbolic Equations," in Math. Comp., vol. 33, no. 146 (April 1979), pp. 647-658
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11. HARDWARE REQUIREMENTS
USCD1224/01
Compiling, loading, and executing the demonstration program required a minimum main storage of 6 Mbytes.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
USCD1224/01 FORTRAN-77
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13. SOFTWARE REQUIREMENTS
USCD1224/01
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
USCD1224/01
Information file
Double precision files:
DLSODI_MAIN.exe Executable file
DLSODI_MAIN.f  Test Source file
DLSODI_OUT.aut Authors output file
DLSOIBT_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
SLSODI_MAIN.exe Executable file
SLSODI_MAIN.f  Test source file
SLSODI_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.