USCD1223 LSODE.
LSODE, 1st Order Stiff or Non-Stiff Ordinary Differential Equations System Initial Value Problems
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHODS, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, 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 |
|---|---|---|---|
| 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.
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.
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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USCD1223/01
At the NEA-DB the demonstration program included in this package ran on a PC Windows Xeon in a few seconds.[ top ]
7. UNUSUAL FEATURES
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.
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.
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.
[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.
[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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USCD1223/01
Compiling, loading, and executing the demonstration program required a minimum main storage of 5 Mbytes.[ top ]
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USCD1223/01
Information fileDouble 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
Keywords: algorithms, initial-value problems, numerical solution, ordinary differential equations.