Computer Programs

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHODS, RESTRICTIONS, CPU, FEATURES, RELATED OR AUXILIARY PROGRAMS, STATUS, REFERENCES, REQUIREMENTS, LANGUAGE, OPERATING SYSTEM, OTHER RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES

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To submit a request, click below on the link of the version you wish to order. Rules for end-users are
available here.

Program name | Package id | Status | Status date |
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LSODI | USCD1224/01 | Tested | 23-SEP-2005 |

Machines used:

Package ID | Orig. computer | Test computer |
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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.

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.

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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USCD1224/01

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.

[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

[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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USCD1224/01

Compiling, loading, and executing the demonstration program required a minimum main storage of 6 Mbytes.[ top ]

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USCD1224/01

Information fileDouble 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

Keywords: algorithms, initial-value problems, numerical solution, ordinary differential equations.