fchamp
======

direction field of a 2D first order ODE



Calling Sequence
~~~~~~~~~~~~~~~~


::

    fchamp(f,t,xr,yr,[arfact,rect,strf])
    fchamp(f,t,xr,yr,<opt_args>)




Arguments
~~~~~~~~~

:f An external (function or character string) or a list which
describes the ODE.
    :- It can be a function name `f`, where `f` is supposed to be a
      function of type `y=f(t,xy [p1,..pn])`. `f` returns a column vector of
      size 2, `y`, which gives the value of the direction field `f` at point
      `xy=[x,y]` and at time `t`.
    : :- It can also be an object of type list, `list(f,P1,..Pn)` where
      `f` is a function of type `y=f(t,xy,p1,..pn)` and `Pi` gives the value
      of the parameter `pi`.
    :

: :t The selected time.
: :xr,yr Two row vectors of size n1 and n2 which define the grid on
  which the direction field is computed.
: :<opt_args> This represents a sequence of statements
  `key1=value1,key2=value2`, ... where `key1`, `key2,...` can be one of
  the following: arfact, rect, strf (see below).
: :arfact,rect,strf Optional arguments, see `champ`.
:



Description
~~~~~~~~~~~

`fchamp` is used to draw the direction field of a 2D first order ODE
defined by the external function `f`. Note that if the ODE is
autonomous, argument `t` is useless, but it must be given.

Enter the command `fchamp()` to see a demo.



Sample
~~~~~~



Examples
~~~~~~~~


::

    `deff`_("[xdot] = derpol(t,x)",..
            ["xd1 = x(2)";..
             "xd2 = -x(1) + (1 - x(1)**2)*x(2)";..
             "xdot = [ xd1 ; xd2 ]"])
    xf= -1:0.1:1;
    yf= -1:0.1:1;
    fchamp(derpol,0,xf,yf)



::

    `deff`_("[xdot] = derpol(t,x)",..
            ["xd1 = x(2)";..
             "xd2 = -x(1) + (1 - x(1)**2)*x(2)";..
             "xdot = [ xd1 ; xd2 ]"])
    xf= -1:0.1:1;
    yf= -1:0.1:1;
    `clf`_()
    fchamp(derpol,0,xf,yf,1,[-2,-2,2,2],"011")




See Also
~~~~~~~~


+ `champ`_ 2D vector field plot
+ `champ1`_ 2D vector field plot with colored arrows


.. _champ: champ.html
.. _champ1: champ1.html