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NESC0705 EPISODE-B.

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

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1. NAME OR DESIGNATION OF PROGRAM:  EPISODE-B.
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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-B NESC0705/01 Tested 01-JUL-1979

Machines used:

Package ID Orig. computer Test computer
NESC0705/01 IBM 360 series IBM 360 series
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3. DESCRIPTION OF PROBLEM OR FUNCTION

EPISODEB is a package of eight  subroutines for the numerical solution of the initial value problem  for systems of first order ordinary differential equations whose Jacobian matrices are banded or can be approximated by band matrices. The package can be used for either stiff or non-stiff systems whose Jacobians can be approximated by band matrices. It is  especially suited to problems with intermittent high-speed transients or waves.
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4. METHOD OF SOLUTION

EPISODEB contains both a variable-step, variable-order, backward differentiation method of orders one through five and a variable-step, variable-order, implicit Adams method of orders one through twelve. The user may select either method to solve a stiff or a non-stiff system. The user may also select from four nonlinear system solvers.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The Jacobian is assumed to be banded. Because the step-size is truly variable, EPISODEB is best suited to problems with intermittent high-speed transients or waves. Smooth or linear problems can lead to high overhead costs. Current dimensioning allows for 100 simultaneous equations. The documentation and comments in EDRIVB show how to alter the limit on the system size and the bandwidth. Limits on the bandwidth and total storage also are described in detail in UCID-30132.
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6. TYPICAL RUNNING TIME

Less than 1 minute is needed to compile and execute the sample problem.
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7. UNUSUAL FEATURES OF THE PROGRAM

The user may select from two integration methods (for stiff and non-stiff problems), and from four nonlinear system solvers. A flexible driver (subroutine EDRIVE) 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 quasi-relative error may be controlled. EDRIVB controls the integration process and prints any error messages.
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8. RELATED AND AUXILIARY PROGRAMS

EPISODE (NESC Abstract 675) for systems with a full Jacobian and LSODE (NESC Abstract 592) for systems with either a full or banded Jacobian matrix.
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9. STATUS
Package ID Status date Status
NESC0705/01 01-JUL-1979 Tested at NEADB
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10. REFERENCES

G.D. Byrne, and A.C. Hindmarsh,
EPISODEB: An Experimental Package for the Integration of Systems of
Ordinary Differential Equations with Banded Jacobians,
UCID-30132, April 1976.
A.C. Hindmarsh and G.D. Byrne,
EPISODE: An Experimental Package for the Integration of Systems of
Ordinary Differential Equations,
UCID-30112, May 1975.
A.C. Hindmarsh,
Banded Linear Systems with Pivoting,
UCID-30060, Rev. 1, May 1976.
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, Association for Computing Machinery Transactions on
Mathematical Software,
Vol. 1, pp. 71-96, March 1975. (Also in UCRL-75652, April 1974).
G.D. Byrne and A.C. Hindmarsh,
An Annotated List of ODE System Solvers,
National Energy Software Center Note 81-71, August 13, 1981.
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11. MACHINE REQUIREMENTS

102K bytes are used to execute the double- precision version of the sample problem.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0705/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  OS/360,370.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The
code is heavily commented. An auxiliary routine, CONVRT, and its driver are provided to change precision from double to single. The user then need only change UROUND in subroutine EDRIVB as indicated  in the code. CDC6600-7000, DEC PDP10, or UNIVAC1100 versions can be  prepared from the IBM version with only minor changes. If EPISODE is to be used on other systems, UROUND (the machine unit roundoff) may need to be evaluated and set in subroutine EDRIVB. The package contains an auxiliary subroutine, MACHIN, and its driver (supplied to NESC by L.F. Shampine and M.K. Gordon of SLA) which may be adapted to calculate or verify UROUND. Program-supplied error messages and the output of the sample problem are written on logical unit 3.
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15. NAME AND ESTABLISHMENT OF AUTHOR

G.D. Byrne
Department of Mathematics and Statistics &
Department of Chemical and Petroleum Engineering
University of Pittsburg
Pittsburg, Pennsylvania 15260
A.C. Hindmarsh, L-310
Numerical Mathematics Group
Lawrence Livermore Laboratory
P.O. Box 808
Livermore, California 94550
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16. MATERIAL AVAILABLE
NESC0705/01
File name File description Records
NESC0705_01.001 INFORMATION 16
NESC0705_01.002 SOURCE PROGRAM (F4,EBCDIC) 1764
NESC0705_01.003 DEMONSTRATION PROGRAM (F4,EBCDIC) 196
NESC0705_01.004 SAMPLE PROBLEM PRINTED OUTPUT 161
NESC0705_01.005 CONVERT -- SOURCE PROGRAM (F4,EBCDIC) 129
NESC0705_01.006 CONVERT -- CONVERTED SOURCE (AS AN OUTPUT) 1764
NESC0705_01.007 MACHIN -- SOURCE PROGRAM (F4,EBCDIC) 28
NESC0705_01.008 JCL 21
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

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