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NESC0731 SUPORT

SUPORT, Solution of Linear 2 Point Boundary Value Problems, Runge-Kutta-Fehlberg Method

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1. NAME OR DESIGNATION OF PROGRAM:  SUPORT
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2. COMPUTERS
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Program name Package id Status Status date
SUPORT NESC0731/02 Tested 01-APR-1979

Machines used:

Package ID Orig. computer Test computer
NESC0731/02 IBM 360 series IBM 360 series
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3. DESCRIPTION OF PROBLEM OR FUNCTION

SUPORT  solves  a  system  of
linear  two-point  boundary-value  problems   subject  to  general
separated boundary conditions.
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4. METHOD OF SOLUTION

The  method  of solution  uses  superposition
coupled with  an orthonormalization procedure and  a variable-step
Runge-Kutta-Fehlberg   integration   scheme.     Each   time   the
superposition   solutions   start   to    lose   their   numerical
independence, the vectors are reorthonormalized before integration
proceeds.  The  underlying principle of  the algorithm is  then to
piece  together   the  intermediate   (orthogonalized)  solutions,
defined  on  the  various  subintervals,  to  obtain  the  desired
solution.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The boundary-value
problem  must  be  linear  and the  boundary  conditions  must  be
separated.   The  number  of  equations which  can  be  solved  is
dependent upon the main storage available.
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6. TYPICAL RUNNING TIME

Examples  in  the   reference  report  give
CDC6600 running times from less than 0.1 to as long as 52 seconds.
The sample  problem executed  by the  NESC took  26 seconds  on an
IBM370/195.
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7. UNUSUAL FEATURES OF THE PROGRAM

The orthonormalization procedure
is  used   to  overcome   the  numerical   instabilities  normally
associated with  initial-value  procedures for  solving  boundary-
value problems.
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8. RELATED AND AUXILIARY PROGRAMS:  SUPORT  is a  stand-alone set  of
subroutines.
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9. STATUS
Package ID Status date Status
NESC0731/02 01-APR-1979 Tested at NEADB
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10. REFERENCES

M. R. Scott and H. A. Watts, SUPORT - A Code for Two-
Point   Boundary-Value  Problems   via  Orthonormalization,   SAND
75-0198, June 1975.
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11. MACHINE REQUIREMENTS:  5500  (octal) words  (CDC6600), 116K  bytes
(IBM370)
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0731/02 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:     SCOPE    3.3
(CDC6600), OS/370 (IBM370).
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

   The
user  must   supply  subroutines   FMAT  and   GVEC  to   evaluate
derivatives.
   The CDC6600  version contains  a COMPASS as  well as  a FORTRAN
version of function DOTPRO.  DOTPRO  computes the inner product of
two vectors.  Whenever possible, an Assembly coded version of this
subroutine should be used.
   There are  several machine-dependent constants  used throughout
the code.   These are listed  in the  comment section of  the code
along with the  suggested values for other  computers.  Except for
these constants, the code is virtually machine-independent.
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15. NAME AND ESTABLISHMENT OF AUTHORS

   6600          M. R. Scott and H. A. Watts
                 Applied Mathematics Division - 2642
                 Sandia Laboratories
                 Albuquerque, New Mexico  87115
   370           L. Eyberger
                 National Energy Software Center
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439
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16. MATERIAL AVAILABLE
NESC0731/02
File name File description Records
NESC0731_02.001 INFORMATION 10
NESC0731_02.002 SOURCE PROGRAM (F4,EBCDIC) 3339
NESC0731_02.003 DRIVER ROUTINES (F4,EBCDIC) 62
NESC0731_02.004 JCL 34
NESC0731_02.005 SAMPLE PROBLEM PRINTED OUTPUT 23
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: boundary-value problems, differential equations, initial-value problems, orthogonal transformation.