USCD1230 LSODKR
LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration with Rootfinding
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHODS, RESTRICTIONS, CPU, UNUSUAL FEATURES, RELATED OR AUXILIARY PROGRAMS, STATUS, REFERENCES, REQUIREMENTS, LANGUAGE, OPERATING SYSTEM, OTHER RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES
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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.
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.
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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USCD1230/01
At the NEA-DB the demonstration program included in this package ran on a PC Windows Xeon in a few seconds.[ top ]
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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.
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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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.
[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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USCD1230/01
Compiling, loading, and executing the demonstration program required a minimum main storage of 5 Mbytes.[ top ]
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USCD1230/01
LSODKR.inf this info fileDouble 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
Keywords: algorithms, initial-value problems, numerical solution, ordinary differential equations.