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ESTS0264 LSODKR-ESTSC.

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

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1. NAME OR DESIGNATION OF PROGRAM:  LSODKR.
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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
LSODKR-ESTSC ESTS0264/01 Tested 01-AUG-1996

Machines used:

Package ID Orig. computer Test computer
ESTS0264/01 IBM PC PC Pentium 100
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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,
c) LSODKR includes the ability to find roots of given functions of the solution during the integration.
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4. METHOD OF SOLUTION

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:  NONE.
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6. TYPICAL RUNNING TIME:  Highly dependent on machine and problems.
ESTS0264/01
The example program supplied with the package has been  executed at the NEA/DB on a PC DELL Pentium processor of 99 MHz under MS-DOS 6.2 A few seconds are required to run both the single (program SLKREX) and the double precision (program DLKREX) versions  of the example program.
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7. UNUSUAL FEATURES OF THE PROGRAM

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 AND AUXILIARY PROGRAMS

LSODKR is similar to a LSODPK (NESC9624) in the use of Krylov methods with both Adams and BDF integration; it is similar to LSODAR in its rootfinding ability. Uses some LINPACK routines; the package supplied includes a
condensed version of SLATEC error message handling routines.
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9. STATUS
Package ID Status date Status
ESTS0264/01 01-AUG-1996 Tested at NEADB
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10. REFERENCES

- Peter N. Brown and Alan C. Hindmarsh:
  Reduced Storage Matrix Methods in Stiff ODE Systems,
  J. Appl. Math & Comp., 31 (1988), pp. 40-91
- L.L.N.L. Report UCRL-95088, Rev.1, June 1987
- Alan C> Hindsmarsh:
  ODEPARCK, A Systematized Collection of ODE Solvers, in Scientific
Computing, R.S. Stepleman et al. (Eds.), North-Holland, Amsterdam,    1983, pp. 55-64
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11. MACHINE REQUIREMENTS:  NONE.
ESTS0264/01
The program LSODKR was installed compiled and executed  on a PC DELL Optiplex GXM 5100, with a Pentium processor of 99 MHz,  base memory 640 Kbyte and extended memory 16 MByte. The filesizes of the single precision program SLKREX.EXE and of the corresponding double precision version DLKREX.EXE, created using the Lahey F77L/EM-32 compiler and linker and activating the option "-stub runb" at linking time, are respectively 320 Kbyte and 339 Kbyte.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
ESTS0264/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  DOS - no system dependence.
ESTS0264/01
The program LSODKR was installed, compiled/linked and executed in a PC-DELL Pentium processor of 99 MHz, under MS-DOS 6.2; the source files were compiled and linked using the Lahey F77L/EM-32 compiler (Version 5.20) and linker (Version 5.1L).
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:  none.
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15. NAME AND ESTABLISHMENT OF AUTHORS

   A.D. Hindmarsh and P.N. Brown
   Lawrence Livermore National Lab.
   Numerical Mathematics Group, C.M.R.D.
   CA (United States)
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16. MATERIAL AVAILABLE
ESTS0264/01
File name File description Records
ESTS0264_01.001 Information file of program LSODKR 239
ESTS0264_01.002 Source (single precision) of the example prb 313
ESTS0264_01.003 Source (single precision) of the LSODKR rout 5265
ESTS0264_01.004 Source (single precision) some LINPACK rout 562
ESTS0264_01.005 Executable (single precision) example prog. 0
ESTS0264_01.006 Printout file - example program (double) 83
ESTS0264_01.007 Source (double precision) of the example prb 333
ESTS0264_01.008 Source (double precision) of the LSODKR rout 5268
ESTS0264_01.009 Source (double precision) some LINPACK rout 564
ESTS0264_01.010 Executable (double precision) example prog. 0
ESTS0264_01.011 Printout file - example program (single) 83
ESTS0264_01.012 Lahey aux. file of runtime errors 0
ESTS0264_01.013 DOS file-names 12
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: ordinary differential equations.