ode command-line options
The command-line options to
ode are listed below. There are
several sorts of option:
- Options affecting the way in which input is read.
- Options affecting the format of the output.
- Options affecting the choice of numerical solution scheme, and the
error bounds that will be imposed on it.
- Options that request information.
The following option affects the way input is read.
- ‘-f filename’
- ‘--input-file filename’
- Read input from filename before reading from standard input.
The following options affect the output format.
- ‘-p significant-digits’
- ‘--precision significant-digits’
- (Positive integer, default 6.) When printing numerical results, use a
precision specified by significant-digits. If this option is
given, the print format will be scientific notation.
- Print a title line at the head of the output, naming the columns. If this option is given, the print format will be scientific notation.
The following options specify the numerical integration scheme. Only
one of the three basic option ‘-R’, ‘-A’, and ‘-E’ may be
specified. The default is ‘-R’ (Runge–Kutta–Fehlberg).
- ‘-R [stepsize]’
- ‘--runge-kutta [stepsize]’
- Use a fifth-order Runge–Kutta–Fehlberg algorithm, with an adaptive
stepsize unless a constant stepsize is specified. When a constant
stepsize is specified and no error analysis is requested, then a
classical fourth-order Runge–Kutta scheme is used.
- ‘-A [stepsize]’
- ‘--adams-moulton [stepsize]’
- Use a fourth-order Adams–Moulton predictor–corrector scheme, with an
adaptive stepsize unless a constant stepsize, stepsize, is
specified. The Runge–Kutta–Fehlberg algorithm is used to get past
`bad' points (if any).
- ‘-E [stepsize]’
- ‘--euler [stepsize]’
- Use a `quick and dirty' Euler scheme, with a constant stepsize. The
default value of stepsize is 0.1. Not recommended for serious
The error bound options ‘-r’ and ‘-e’ (see below) may not
be used if ‘-E’ is specified.
- ‘-h hmin [hmax]’
- ‘--step-size-bound hmin [hmax]’
- Use a lower bound hmin on the stepsize. The numerical scheme will
not let the stepsize go below hmin. The default is to allow the
stepsize to shrink to the machine limit, i.e., the minimum nonzero
double-precision floating point number. The optional argument
hmax, if included, specifies a maximum value for the stepsize.
It is useful in preventing the numerical routine from skipping
quickly over an interesting region.
The following options set the error bounds on the numerical solution
- ‘-r rmax [rmin]’
- ‘--relative-error-bound rmax [rmin]’
- ‘-e emax [emin]’
- ‘--absolute-error-bound emax [emin]’
- The ‘-r’ option sets an upper bound on the relative single-step
error. If the ‘-r’ option is used, the relative single-step error
in any dependent variable will never exceed rmax (the default for
which is 10^(-9)). If this should occur, the solution will be
abandoned and an error message will be printed. If the stepsize is
not constant, the stepsize will be decreased `adaptively', so that the
upper bound on the single-step error is not violated. Thus, choosing a
smaller upper bound on the single-step error will cause smaller
stepsizes to be chosen. A lower bound rmin may optionally be
specified, to suggest when the stepsize should be increased (the default
for rmin is rmax/1000). The ‘-e’ option is similar to
‘-r’, but bounds the absolute rather than the relative single-step
- Suppress the ceiling on single-step error, allowing
continue even if this ceiling is exceeded. This may result in large
Finally, the following options request information.
- Print a list of command-line options, and then exit.
- Print the version number of
ode and the plotting utilities
package, and exit.