The Plotutils Package - ode Invocation

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## `ode` command-line options

The command-line options to `ode` are listed below. There are several sorts of option:

1. Options affecting the way in which input is read.
2. Options affecting the format of the output.
3. Options affecting the choice of numerical solution scheme, and the error bounds that will be imposed on it.
4. 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.
``-t'`
``--title'`
  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 applications. 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 scheme.

``-r rmax [rmin]'`
``--relative-error-bound rmax [rmin]'`
``-e emax [emin]'`
``--absolute-error-bound emax [emin]'`
  @ifnottex 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 error.
``-s'`
``--suppress-error-bound'`
  Suppress the ceiling on single-step error, allowing `ode` to continue even if this ceiling is exceeded. This may result in large numerical errors.

Finally, the following options request information.

``--help'`
  Print a list of command-line options, and then exit.
``--version'`
  Print the version number of `ode` and the plotting utilities package, and exit.

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