NESC0705 EPISODE-B.
EPISODE-B, 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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To submit a request, click below on the link of the version you wish to order.
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| 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.
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.
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.
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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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.
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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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.
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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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.
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
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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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 |
Keywords: Adams method, banded matrix, initial-value problems, numerical solution, ordinary differential equations.