NESC0652 STFODE/COLODE
STFODE-COLODE, 1st Order Stiff Ordinary Differential Equation System by Collocation Method
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 AUTHORS, MATERIAL, CATEGORIES
[ top ]
[ top ]
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 |
|---|---|---|---|
| STFODE-COLODE | NESC0652/02 | Tested | 01-APR-1978 |
Machines used:
| Package ID | Orig. computer | Test computer |
|---|---|---|
| NESC0652/02 | IBM 370 series | IBM 370 series |
[ top ]
[ top ]
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.
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.
[ top ]
[ top ]
[ top ]
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.
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.
[ top ]
[ top ]
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.
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.
[ top ]
[ top ]
[ top ]
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.
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.
[ top ]
[ top ]
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 |
Keywords: collocation method, nonlinear problems, numerical solution, ordinary differential equations, polynomials.