Re: Back Euler with error control

"elvis.lu@xxxxxxxxx" wrote:
>
> Hi ,everyone. I'm trying to solve an ODE with back euler with given
> accuracy tolerance. This means I should choose the time matching step
> adaptively, but I don't know how to do it. Does anybody know a
> practical Back Euler method with error control?

Your brain must have fogged over by PS recipes, however it seems
unlikely that your homework was meant to outfit a primitive integrator
with monster sized correctors. Outside the academics, practical error
control usually boils down to a simple trial & error repetition.
In a nutshell:

Pick an h, integrate, then repeat with h/2, compare the results (at h)
against tolerances (rel & abs), proceed if met, else cut h in half again
until tolerance are met, and so on.

.