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PSR-0078 FORSIM-6.

FORSIM-6, Automatic Solution of Coupled Differential Equation System

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1. NAME OR DESIGNATION OF PROGRAM:  FORSIM-6.
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2. COMPUTERS
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Program name Package id Status Status date
FORSIM-6 PSR-0078/01 Tested 18-OCT-1983

Machines used:

Package ID Orig. computer Test computer
PSR-0078/01 CDC 7600 CDC 7600
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3. DESCRIPTION OF PROBLEM OR FUNCTION

The FORSIM program is a versatile package which automates the solution of coupled differential equation systems. The independent variables are time, and up to three space coordinates, and the equations may be any mixture of partial and/or ordinary differential equations. The philosophy of the program is to provide a tool which will solve a system of differential equations for a user who has basic but unspecialized knowledge of numerical analysis and FORTRAN.

The equations to be solved, together with the initial conditions and any special instructions, may be specified by the user in a single FORTRAN subroutine, although he may write a number of routines if this is more suitable. These are then loaded with the control routines, which perform the solution and any requested input and output.
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4. METHOD OF SOLUTION

Partial differential equations are automatically converted into sets of coupled ordinary differential equations by variable order discretization in the spatial dimensions. These and other ordinary differential equations are integrated continuously in time using efficient variable order, variable step, error-controlled algorithms.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:
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6. TYPICAL RUNNING TIME

NEA-DB executed the three test cases included in the package on CDC 7600. Only cases 1 and 2 converged. For these the following execution times (CPU) were found:
Case 1: 2.5 seconds; case 2: 72.7 seconds.
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7. UNUSUAL FEATURES OF THE PROGRAM

For external use, the small number of local software features peculiar to CRNL in FORSIM have been deactivated. They include PLOT and PLOT3D; the CALCOMP interface routines; OFLOW, a routine to override abortive failure; and IRCP, an assembly language routine which does field length management by dynamically adjusting the blank common working storage area according to the size of the equation set involved.

This latter means that external users must specify a fixed size for blank common working storage by declaring it in subroutine SIZE. This should be defined as an installation default and redefined by the user as necessary following the manual section 9.4, and adding three addition statements in SIZE:

                     COMMON BLANK(1000)
                     COMMON/NEQN/NEQN,NBLANK
                     DATA NBLANK/1000/

For external versions, the field management routines have been modified to merely check the size of blank common, and any messages  concerning field length should be interpreted as meaning blank common length. A minimum size for blank common is 8n where n is the  number of users' equations. Providing the data statement is equal to the declared size, FORSIM will attempt to find an integration algorithm which fits in the available storage.
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8. RELATED AND AUXILIARY PROGRAMS:
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9. STATUS
Package ID Status date Status
PSR-0078/01 18-OCT-1983 Tested at NEADB
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10. REFERENCES:
PSR-0078/01, included references:
-  M. B. Carver et al.:
    The FORSIM-6 Simulation Package for the Automated Solution of
    Arbitrarily Defined Partial and/or Ordinary Differential
    Equations Systems.
    AECL-5821 (Revised and Reprinted May 1979)
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11. MACHINE REQUIREMENTS

Basic FORSIM with room for 1000 equations requires about CM70000 (octal) to load and execute. As the user routines and any FORSIM library routines loaded will increase this slightly, default memory CM100000 (octal) (or CM parameter on job card absent) is recommended for use at CRNL.

For jobs with a large number of equations using the sophisticated Hindmarsh/Gear/Carver/Reid algorithm, more memory may be required. This presents no problem, as the first run is normally an exploratory trial, and FORSIM will report on how much memory is required. If insufficient job card field length is available, FORSIM will swith algorithms until a suitable one is found (Runge-Kutta will always run once the program is loaded).

For extremely large user routines, it is conceivable that the program will not even load. If such a possibility is expected, it is best to use the K parameter on the job card instead of CM. Kkkk, on  the job card permits the job to use kkkk00 (octal) kiloword seconds  during execution and allows it to occupy up to 300000(octal) CM until this KWS limit (CM*(T+IO)) is exhausted. FORSIM will report on required CM for the next run.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
PSR-0078/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:
NOS 1.4-531 (CDC 7600).
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHOR

M.B. Carver, D.G. Stewart, J.M. Blair, W.N. Selander
Chalk River Nuclear Laboratories
Chalk River, Ontario KOJ.1J0, Canada
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16. MATERIAL AVAILABLE
PSR-0078/01
File name File description Records
PSR0078_01.003 FORSIM-6 INFORMATION FILE 28
PSR0078_01.004 FORSIM-6 SOURCE (FORTRAN-4) 6723
PSR0078_01.005 TEST ROUTINE 1 (UPDATE FORMAT) 28
PSR0078_01.006 TEST CASE DATA 1 12
PSR0078_01.007 TEST ROUTINE 2 (UPDATE FORMAT) 66
PSR0078_01.008 TEST CASE DATA 2 16
PSR0078_01.009 TEST ROUTINE 3 (UPDATE FORMAT) 85
PSR0078_01.010 TEST CASE DATA 3 20
PSR0078_01.011 FORSIM-6 JCL FOR TEST CASE EXECUTION 86
PSR0078_01.012 TEST CASE OUTPUT 1 609
PSR0078_01.013 TEST CASE OUTPUT 2 1297
PSR0078_01.014 TEST CASE OUTPUT 3 205
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: differential equations, ordinary differential equations, partial differential equations.