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USCD1230 LSODKR

LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration with Rootfinding

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1. NAME OR DESIGNATION OF PROGRAM:  LSODKR.
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2. COMPUTERS
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Program name Package id Status Status date
LSODKR USCD1230/01 Tested 23-SEP-2005

Machines used:

Package ID Orig. computer Test computer
USCD1230/01 IBM PC PC Windows
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3. DESCRIPTION OF PROGRAM OR FUNCTION

LSODKR is a new initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following:
a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations,
b) within the corrector iteration, LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, The nonlinear iteration method-switching differs from the method-switching in LSODA and LSODAR, but provides similar savings by using the cheaper method in the non-stiff regions of the problem.
c) LSODKR includes the ability to find roots of given functions of the solution during the integration.
d) LSODKR also improves on the Krylov methods in LSODPK by offering the option to save and reuse the approximate Jacobian data underlying the preconditioner.
  
The LSODKR 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. Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fixpoint iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
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6. TYPICAL RUNNING TIME
USCD1230/01
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

Krylov iterative methods with user-supplied preconditioning. Automatic switching between Newton and functional iteration. Rootfinding feature coupled with system integration.
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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
USCD1230/01 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
USCD1230/01
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
USCD1230/01 FORTRAN-77
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13. SOFTWARE REQUIREMENTS
USCD1230/01
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
USCD1230/01
LSODKR.inf  this info file
Double precision files:
DLSODKR_MAIN.exe Executable file
DLSODKR_MAIN.f Test Source file
DLSODKR_OUT.aut Author's output file
DLSODKR_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
SLSODKR_MAIN.exe Executable file
SLSODKR_MAIN.f Test source file
SLSODKR_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.