Computer Programs

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHODS, RESTRICTIONS, TYPICAL RUNNING TIME, 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 |
---|---|---|---|

LSODIS | USCD1225/01 | Tested | 23-SEP-2005 |

Machines used:

Package ID | Orig. computer | Test computer |
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USCD1225/01 | IBM PC | PC Windows |

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3. DESCRIPTION OF PROGRAM OR FUNCTION

LSODIS 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. LSODIS 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. LSODIS, written jointly with S. Balsdon, solves linearly implicit systems in which the matrices involved are all assumed to be sparse. LSODIS determines the sparsity structure or accepts it from the user, and uses parts of the Yale Sparse Matrix Package to solve the linear systems that arise, by a direct method. The LSODIS source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available.

LSODIS 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. LSODIS 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. LSODIS, written jointly with S. Balsdon, solves linearly implicit systems in which the matrices involved are all assumed to be sparse. LSODIS determines the sparsity structure or accepts it from the user, and uses parts of the Yale Sparse Matrix Package to solve the linear systems that arise, by a direct method. The LSODIS 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 -1 .le. x .le. 1, t .ge. 0.

Here eta = 0.05.

Boundary conditions: u(-1,t) = u(1,t) and du/dx(-1,t) = du/dx(1,t).

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 -1 .le. x .le. 1, t .ge. 0.

Here eta = 0.05.

Boundary conditions: u(-1,t) = u(1,t) and du/dx(-1,t) = du/dx(1,t).

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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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," 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," Math. Comp., vol. 33, no. 146 (April 1979), pp. 647-658.

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USCD1225/01

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

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USCD1225/01

Information fileDouble precision files:

DLSODIS_MAIN.exe Executable file

DLSODIS_MAIN.f Test Source file

DLSODIS_OUT.aut Authors output file

DLSODIS_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

SLSODIS_MAIN.exe Executable file

SLSODIS_MAIN.f Test source file

SLSODIS_OUT.nea NEA output file

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