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NESC0652 STFODE/COLODE

STFODE-COLODE, 1st Order Stiff Ordinary Differential Equation System by Collocation Method

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1. NAME OR DESIGNATION OF PROGRAM:  STFODE/COLODE
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2. COMPUTERS
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Program name Package id Status Status date
STFODE-COLODE NESC0652/02 Tested 01-APR-1978

Machines used:

Package ID Orig. computer Test computer
NESC0652/02 IBM 370 series IBM 370 series
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3. DESCRIPTION OF PROBLEM OR FUNCTION

COLODE   is    a   subroutine
intended  primarily  for  solving  first-order  systems  of  stiff
differential equations by collocation methods.  STFODE is a driver
routine written to simplify the use of COLODE.
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4. METHOD OF SOLUTION

The principal subroutine COLODE uses one-step
collocation to integrate  over a given interval,  taking two equal
steps at a time.  The collocation  method, chosen either by COLODE
or by the user,  is fixed during the integration, but  the size of
each pair of steps is automatically varied.  At each step a vector
of continuous nth degree piecewise  polynomials is made to satisfy
the o.d.e. at n Gauss-Legendre  or Radau (right-end) points, where
1.LE.n.LE.12.   The Gauss-Legendre  methods  are  a-stable and  of
order 2n,  while the  Radau methods are  strongly a-stable  and of
order 2n-1.
   STFODE, the driver for COLODE, is  intended for users who never
want to supply a Jacobian subroutine or select the method.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Storage
requirements limit  the number of equations  to about 100  for the
CDC6600 version.
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6. TYPICAL RUNNING TIME

Running time varies widely  with the number
and  type  of  equations  and the  magnitude  and  type  of  error
tolerance requested.
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7. UNUSUAL FEATURES OF THE PROGRAM

The user  has two  options which
are uncommon to o.d.e. solvers.  First, the user may indicate that
the Jacobian of the derivative vector is constant, allowing COLODE
to economize on Jacobian evaluations.  Second, the user may choose
to obtain results  only at the end of the  integration interval or
to have intermediate returns after each pair of steps yielding the
results from both steps.
   COLODE is  particularly effective  on stiff  problems with  (a)
extremely rapidly  decaying solution  components, (b)  all nonreal
eigenvalues of the  Jacobian, (c) periodic transients,  or (d) any
stiff problem with very small error tolerances.
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8. RELATED AND AUXILIARY PROGRAMS

COLODE  actually  uses   a  third
subroutine, TWOSTP, to advance the solution two steps.
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9. STATUS
Package ID Status date Status
NESC0652/02 01-APR-1978 Tested at NEADB
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10. REFERENCES

B. L.  Hulme, Discrete Galerkin and  Related One-step
Methods  for  Ordinary  Differential   Equations,  Mathematics  of
Computation, Vol. 26, pp. 881-891, 1972.
             B. L. Hulme and S.  L. Daniel, COLODE:  A Collocation
Subroutine  for  Ordinary   Differential  Equations,  SAND74-0380,
December 1974.
             B. L. Hulme and S.  L. Daniel, Using STFODE/COLODE to
Solve Stiff Ordinary Differential Equations, SAND74-0381, December
1974.
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11. MACHINE REQUIREMENTS

CDC6600  version load  used 24,500  (octal)
words, sample problem execution  15,000 (octal) words.  IBM360/370
version sample problem execution used 140K bytes.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0652/02 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:     SCOPE    3.3
(CDC6600), OS/360 (IBM360).
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

Besides the Gauss-Legendre and Radau  abscissas in DATA statements
of TWOSTP,  there are  machine constants  for the  roundoff level,
twice the roundoff level, the underflow level, and 10**4 times the
underflow level in  DATA statements of COLODE and  TWOSTP.  In the
original CDC6600  version, STFODE has  one call, COLODE  has three
calls, and  TWOSTP has  one call  of ERRCHK,  a system  subroutine
which processes error  messages.  These five calls  of ERRCHK must
be changed to  conform with local installation  practices.  In the
IBM360 version, these were changed to PRINT statements.
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15. NAME AND ESTABLISHMENT OF AUTHORS

   6600          B. L. Hulme and S. L. Daniel
                 Numerical Mathematics Division 5122
                 Sandia Laboratories
                 P. O. Box 5800
                 Albuquerque, New Mexico  87115
   360           A. J. Strecok
                 National Energy Software Center
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439
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16. MATERIAL AVAILABLE
NESC0652/02
File name File description Records
NESC0652_02.001 SUBROUTINES (F4,EBCDIC) 1161
NESC0652_02.002 DEMONSTRATION PROG. FOR STFODE (F4,EBCDIC) 51
NESC0652_02.003 DEMONSTRATION PROG. FOR COLODE (F4,EBCDIC) 58
NESC0652_02.004 PRINTED OUTPUT OF 'STFODE' 27
NESC0652_02.005 PRINTED OUTPUT OF 'COLODE' 27
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: collocation method, nonlinear problems, numerical solution, ordinary differential equations, polynomials.