Compatibility between Maple V, Release 3 and Release 4
The materials in this supplement were prepared in advance of the release
of Maple V, Release 4 (The Power Edition). Release 4 versions of the
worksheets in the supplement were made availble on 1 January 1997.
The Release 4 versions are quite similar to the original worksheets.
Improvements, enhancements, and additions -- including directions for
further investigation (``Points to Ponder'') -- have been added to most
of the worksheets.
(Note that Release 3 worksheets have a .ms extension; Release 4
worksheets use .mws.
The printed version of the Supplement has not yet
been updated; it still provides a reasonable representation of the
content available on the WWW.
A good summary of the new features available in Release 4 can be obtained
from the on-line help page accessed by ?updatesR4. The following
items should be of particular interest:
- plotting routines in the DEtools package have been rewritten
for example (on p. 47) the command
DEplot(ODE, [x,y], x = 1..2, y = 4..6, arrows = THIN):
should be replaced with
DEplot(ODE, y, x = 1..2, y = 4..6, arrows = SMALL):
(for more information, please see the on-line help pages for
DEtools[DEplot], DEtools[DEplot3d], and
DEtools[PDEplot])
- apparent bug in DEplot for solution curves for 2D systems
The revisions that were made to the DEtools package for
Release 4 include the use of arrows=SMALL as the default;
this choice causes an error when the scene= option is used
to request the plot of a solution curve. This problem has been
reported to Maple's Technical Support, and should be fixed in the
next(?) patch; in the meantime, this problem can be avoided by
explicitly specifyng arrows=NONE in the argument list.
- symbolic routines in the DEtools package have been improved
(for more information, please see the on-line help pages for, e.g.,
DEtools[changevar], DEtools[reduceOrder], and
DEtools[convertsys])
- expanded set of numerical methods available via dsolve
the complete list of ``classical'' numerical methods is
- foreuler
- forward Euler method (default classical method)
- heunform
- Heun's formula (aka trapezoidal rule or improved Euler method)
- impoly
- improved polygon method (aka modified Euler method)
- rk2
- second-order classical Runge-Kutta method
- rk3
- third-order classical Runge-Kutta method
- rk4
- fourth-order classical Runge-Kutta method
- adambash
- Adams-Bashford method (a ``predictor'' method)
- abmoulton
- Adams-Bashford-Moulton method (a ``predictor-corrector'' method)
(for more information, please see the on-line help page for
dsolve[classical])
Please report any questions, concerns, or comments to the author; the
e-mail address is
meade@math.sc.edu
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Last modified: 1 January 1997, by
Douglas B. Meade
(meade@math.sc.edu)