I'm solving stiff ODE systems, like
y' = My + f
where M is a large constant matrix and f occasionally changes.
I know that explicit (forward) Euler, RK4 and other usual explicit methods are rarely used to solve these problems because very tiny timesteps are required to avoid instability. I know that implicit methods usually have no such problems.
However, now I would like to know that are there stable (absolutely stable?) explicit methods at all? I'm interested in them even if they are not very accurate.