with either the explicit Euler method or the implicit Euler method.
Using the explicit Euler method I would get the updating scheme
where the eigenvalues of the driving matrix is
For the solution to be stable these need to be less than one which gives the conditions
The last condition doesn't say anything but the first condition seems restrictive since I can't choose as small as possible.
If I instead were to use the implicit Euler method I would get the updating scheme
Now I can't solve for the eigenvalues of this system but I've heard the implicit Euler is unconditionally stable so it shouldn't matter.
So is the answer that I should choose implicit Euler because it is unconditionally stable or am I missing something? The order of consistency of both is 1 so that should not matter.