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NESC0675 EPISODE.

EPISODE, 1st Order Stiff or Non-Stiff Ordinary Differential Equation, Initial Value Problems

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1. NAME OR DESIGNATION OF PROGRAM:  EPISODE.
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2. COMPUTERS
To submit a request, click below on the link of the version you wish to order. Only liaison officers are authorised to submit online requests. Rules for requesters are available here.
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.
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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.
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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.
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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.
NESC0675/02
NEA-DB executed the test case on IBM 3081 in 1 CP sec.
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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.
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8. RELATED AND AUXILIARY PROGRAMS

LSODE (NESC Abstract 592) solves systems with a full or banded Jacobian matrix.
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9. STATUS
Package ID Status date Status
NESC0675/02 21-JUL-1983 Tested at NEADB
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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.
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.
NESC0675/02
72K bytes of main storage are required to execute the test case on IBM 3081.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0675/02 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

OS/360,370
(IBM360,370), VM/CMS (IBM4331), NOS 2.2 (CDC CYBER175), EXEC8 (UNIVAC1100).
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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.
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15. NAME AND ESTABLISHMENT OF AUTHOR

G.D. Byrne
Computing Technology & Services Division
Exxon Research and Engineering Company

A.C. Hindmarsh
Numerical Mathematics Group, L-310
Lawrence Livermore Laboratory
P.O. Box 808
Livermore, California 94550
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16. MATERIAL AVAILABLE
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
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

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