NESC0675 EPISODE.
EPISODE, 1st Order Stiff or Non-Stiff Ordinary Differential Equation, Initial Value Problems
NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES
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| Program name | Package id | Status | Status date |
|---|---|---|---|
| EPISODE | NESC0675/02 | Tested | 21-JUL-1983 |
Machines used:
| Package ID | Orig. computer | Test computer |
|---|---|---|
| NESC0675/02 | IBM 3081 | IBM 3081 |
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3. DESCRIPTION OF PROBLEM OR FUNCTION
EPISODE is a package of eight subroutines for the numerical solution of the initial-value problem for systems of first-order ordinary differential equations. The package can be used for either stiff or non-stiff systems. It is especially suited to problems with intermittent high-speed transients.
EPISODE is a package of eight subroutines for the numerical solution of the initial-value problem for systems of first-order ordinary differential equations. The package can be used for either stiff or non-stiff systems. It is especially suited to problems with intermittent high-speed transients.
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4. METHOD OF SOLUTION
EPISODE contains both a variable-step, variable-order backward differentiation method of orders one through five and variable-step, variable-order implicit Adams method of orders one through twelve. The user may select either method to solve a stiff or non-stiff system. He may also select from four nonlinear system solvers.
EPISODE contains both a variable-step, variable-order backward differentiation method of orders one through five and variable-step, variable-order implicit Adams method of orders one through twelve. The user may select either method to solve a stiff or non-stiff system. He may also select from four nonlinear system solvers.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
Because the stepsize is truly variable, EPISODE is best suited to problems with inter- mittent high-speed transients. Smooth problems can lead to high overhead costs. Current dimensioning allows for 20 simultaneous equations. The documentation and comments in DRIVE show how to alter this limit.
Because the stepsize is truly variable, EPISODE is best suited to problems with inter- mittent high-speed transients. Smooth problems can lead to high overhead costs. Current dimensioning allows for 20 simultaneous equations. The documentation and comments in DRIVE show how to alter this limit.
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6. TYPICAL RUNNING TIME
NESC executed the sample in less than 25 CPU seconds on an IBM4331 and in less than 1 CP second on a CDC CYBER175.
NESC executed the sample in less than 25 CPU seconds on an IBM4331 and in less than 1 CP second on a CDC CYBER175.
NESC0675/02
NEA-DB executed the test case on IBM 3081 in 1 CP sec.[ top ]
7. UNUSUAL FEATURES OF THE PROGRAM
The user may select either of two integration methods (for stiff and non-stiff problems), and from four nonlinear system solvers. A flexible driver (subroutine DRIVE) returns output data at a previously-specified point by interpolation, provides output data by hitting the prescribed output point without interpolation, or returns data after each step. Absolute error, true relative error, or a quasi-relative error may be controlled. DRIVE controls the integration process and prints any error messages.
The user may select either of two integration methods (for stiff and non-stiff problems), and from four nonlinear system solvers. A flexible driver (subroutine DRIVE) returns output data at a previously-specified point by interpolation, provides output data by hitting the prescribed output point without interpolation, or returns data after each step. Absolute error, true relative error, or a quasi-relative error may be controlled. DRIVE controls the integration process and prints any error messages.
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10. REFERENCES
- A.C. Hindmarsh and G.D. Byrne,
EPISODE: An Experimental Package for the Integration of Systems
of Ordinary Differential Equations,
UCID-30112, Rev. 1, April 1977, with Errata.
- G.D. Byrne and A.C. Hindmarsh,
An Annotated List of Some Codes for Solving dy/dt=f(y,t),
y(t0)=y0,
National Energy Software Center Note 81-71, August 13, 1981.
- EPISODE, NESC No. 675.MPL3, EPISODE Tape Description,
National Energy Software Center Note 86-79, July 17, 1986.
- A.C. Hindmarsh and G.D. Byrne,
Applications of EPISODE: An Experimental Package for the
Integration of Systems of Ordinary Differential Equations, in
Numerical Methods for Differential Systems,
L. Lapidus and W.E. Schiesser, Eds., Academic Press, 1976.
(Also published as UCRL-75868, JUNE 1975).
- G.D. Byrne and A.C. Hindmarsh,
A Polyalgorithm for the Numerical solution of Ordinary
Differential Equations, ACM Transactions on Mathematical Software, Vol. 1, pp. 71-96, March 1975. (Also in UCRL-75652, April 1974).
- G.D. Byrne, A.C. Hindmarsh, K. R. Jackson, and H.G. Brown,
Comparative Test Results for Two ODE Solvers - EPISODE and
GEAR, ANL-77-19, March 1977.
- A.C. Hindmarsh and G.D. Byrne,
EPISODE: An Experimental Package for the Integration of Systems
of Ordinary Differential Equations,
UCID-30112, Rev. 1, April 1977, with Errata.
- G.D. Byrne and A.C. Hindmarsh,
An Annotated List of Some Codes for Solving dy/dt=f(y,t),
y(t0)=y0,
National Energy Software Center Note 81-71, August 13, 1981.
- EPISODE, NESC No. 675.MPL3, EPISODE Tape Description,
National Energy Software Center Note 86-79, July 17, 1986.
- A.C. Hindmarsh and G.D. Byrne,
Applications of EPISODE: An Experimental Package for the
Integration of Systems of Ordinary Differential Equations, in
Numerical Methods for Differential Systems,
L. Lapidus and W.E. Schiesser, Eds., Academic Press, 1976.
(Also published as UCRL-75868, JUNE 1975).
- G.D. Byrne and A.C. Hindmarsh,
A Polyalgorithm for the Numerical solution of Ordinary
Differential Equations, ACM Transactions on Mathematical Software, Vol. 1, pp. 71-96, March 1975. (Also in UCRL-75652, April 1974).
- G.D. Byrne, A.C. Hindmarsh, K. R. Jackson, and H.G. Brown,
Comparative Test Results for Two ODE Solvers - EPISODE and
GEAR, ANL-77-19, March 1977.
NESC0675/02, included references:
- A.C. Hindmarsh and G.D. Byrne:EPISODE: An Effective Package for the Integration of System of
Ordinary Differential Equations. UCID-30112, Rev. 1
- L. Eyberger:
Corrections and Enhancements to EPISODE
NESC Note 86-80 (July 17, 1986)
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11. MACHINE REQUIREMENTS
The memory required to execute the sample problem is 252K bytes on an IBM4331 and 21,000 (octal) words on a CDC CYBER175.
The memory required to execute the sample problem is 252K bytes on an IBM4331 and 21,000 (octal) words on a CDC CYBER175.
NESC0675/02
72K bytes of main storage are required to execute the test case on IBM 3081.[ top ]
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS
Auxiliary programs CONVERT and MACHIN are included in the package. CONVERT is used to change precision of the source from double to single and vice versa. CONVERT terminates execution with an end-of- file condition. MACHIN, supplied by L.F. Shampine and M.K. Gordon of SNLA, may be used to verify or calculate UROUND (the machine unit roundoff). The packaged source is set up for IBM systems. The CDC version can be prepared by converting the source to single-precision (via CONVERT) and enabling the appropriate UROUND value and PROGRAM statement in the demonstration program. The UNIVAC version is prepared by enabling the appropriate UROUND value and DEFINE FILE statement in the demonstration program. The UNIVAC-specific modifications were supplied by Sylvia F. Heard of the University of Alabama in Huntsville. If EPISODE is to be used on other systems, the appropriate value for UROUND will need to be provided and set in subroutine DRIVE. Error messages and the sample problem printed output are written to logical unit 3.
Auxiliary programs CONVERT and MACHIN are included in the package. CONVERT is used to change precision of the source from double to single and vice versa. CONVERT terminates execution with an end-of- file condition. MACHIN, supplied by L.F. Shampine and M.K. Gordon of SNLA, may be used to verify or calculate UROUND (the machine unit roundoff). The packaged source is set up for IBM systems. The CDC version can be prepared by converting the source to single-precision (via CONVERT) and enabling the appropriate UROUND value and PROGRAM statement in the demonstration program. The UNIVAC version is prepared by enabling the appropriate UROUND value and DEFINE FILE statement in the demonstration program. The UNIVAC-specific modifications were supplied by Sylvia F. Heard of the University of Alabama in Huntsville. If EPISODE is to be used on other systems, the appropriate value for UROUND will need to be provided and set in subroutine DRIVE. Error messages and the sample problem printed output are written to logical unit 3.
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NESC0675/02
| File name | File description | Records |
|---|---|---|
| NESC0675_02.003 | EPISODE INFORMATION FILE | 32 |
| NESC0675_02.004 | EPISODE SOURCE PART 1 (FORTRAN-4) | 1801 |
| NESC0675_02.005 | EPISODE SOURCE PART 2 (FORTRAN-4) | 129 |
| NESC0675_02.006 | EPISODE SOURCE PART 3 (FORTRAN-4) | 24 |
| NESC0675_02.007 | EPISODE JCL | 13 |
| NESC0675_02.008 | EPISODE OUTPUT OF TEST CASE | 155 |
Keywords: Adams method, initial-value problems, numerical solution, ordinary differential equations.