ode_discrete
============

ordinary differential equation solver, discrete time simulation



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


::

    y=ode("discrete",y0,k0,kvect,f)




Arguments
~~~~~~~~~

:y0 a real vector or matrix (initial conditions).
: :t0 a real scalar (initial time).
: :f an external i.e. function or character string or list.
: :k0 an integer (initial time).
: :kvect an integer vector.
:



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

With this syntax (first argument equal to `"discrete"`) `ode` computes
recursively `y(k+1)=f(k,y(k))` from an initial state `y(k0)` and
returns `y(k)` for `k` in `kvect`. `kvect(1)` must be greater than or
equal to `k0`.

Other arguments and other options are the same as for `ode`, see the
see `ode`_ help.



Examples
~~~~~~~~


::

    y1=[1;2;3]; `deff`_("yp=a_function(k,y)","yp=A*y+B*u(k)")
    A=`diag`_([0.2,0.5,0.9]); B=[1;1;1];u=1:10;n=5;
    y=`ode`_("discrete",y1,1,1:n,a_function);
    y(:,2)-(A*y1+B*u(1))
    
    // Now y evaluates  at [y3,y5,y7,y9]
    y=`ode`_("discrete",y1,1,3:2:9,a_function)




See Also
~~~~~~~~


+ `ode`_ ordinary differential equation solver


.. _ode: ode.html