## from reoccurance relation to a differential equation

Hi,
say I have a reoccurance relation:

$a_{t+1} = f(a_t)$

and I want to try and solve it as a differential eq:

$\frac { da_t }{ dt }\cong \frac { a_{ t+1 }-a_{ t } }{ \Delta t } =\frac { f(a_{ t })-a_{ t } }{ \Delta t } =...$

What $\Delta t$ do I take? can I just use $\Delta t = 1 ..?$

thank you