ODE(1)                   USER COMMANDS                     ODE(1)



NAME
     ode - numerical solution of ordinary differential equations

SYNOPSIS
     ode [ options ... ]

DESCRIPTION
     Ode is a language designed for  solving  the  initial  value
     problem  for  a  family of first-order ordinary differential
     equations.  Three distinct  methods  are  available:  Runge-
     Kutta-Fehlberg  (default),  Adams-Moulton  and  Euler.   The
     Adams-Moulton and Runge-Kutta routines  are  available  with
     adaptive step size.

     Ode reads its program from the standard input.  An ode  pro-
     gram  -- or simply an 'ode' -- consists of a list of expres-
     sions for  evaluating  the  derivatives  of  functions,  and
     optional control statements.

     The command-line flags are:

     -f file
          Read file before reading the standard input.

     -A [step], -R [step], -E [step]
          Use the Adams-Moulton, Runge-Kutta-Fehlberg,  or  Euler
          method,  respectively.  Only one of these may be given.
          The optional step causes the method to be applied  with
          a constant step size.

     -h hmin [hmax]
          Indicates a lower and an optional upper  bound  on  the
          step  size.   The  default  lower  bound is the machine
          limit.

     -r rmax [rmin]
          Sets a  ceiling  for  the  relative  single-step  error
          (default  is  1e-8).   The adaptive methods monitor the
          error to  adjust  the  step  size.   If  the  limit  is
          exceeded  in  any variable, the step is abandoned.  The
          value rmin can be used to force the step size to grow.

     -e emax [emin]
          Similarly for the absolute single-step error.

     -s
          Suppresses the ceiling on single-step error so that the
          program continues if it reaches these limits.

     -p prec
          Values are printed to prec significant figures.




Sun Release 4.1     Last change: Reed College                   1






ODE(1)                   USER COMMANDS                     ODE(1)



     -t
          A title line names the columns.

DIAGNOSTICS
     Mostly self-explanatory.  The biggest exception  is  'syntax
     error',  meaning  there  is  a  grammatical error.  Language
     error messages are of the form

          ode: nnn: message...

     where 'nnn' is the  location  of  the  line  containing  the
     error.   When  the -f flag is used, the phrase '(file)' fol-
     lows the 'nnn' for errors encountered inside the file.  Sub-
     sequently,  when ode begins reading the standard input, line
     numbers start over from one.

     Run-time errors elicit a message describing the problem  and
     the solution is abandoned.

SEE ALSO
     graph(1)
     "Ode User's Manual"

BUGS
     No effort is made to  recover  successfully  from  syntactic
     errors  in  the input.  However, there is a meager effort to
     resynchronize so more than one error can  be  found  in  one
     scan.
























Sun Release 4.1     Last change: Reed College                   2