ordinary differential equation solver, discrete time simulation
y=ode("discrete",y0,k0,kvect,f)
: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. :
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.
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)