I'm concerned with numerical methods for the approximation of semigroup associated to following Cauchy problems (which typically involves unbounded operators): $$ \begin{cases} \dfrac{du}{dt} + Au = 0 \\ \\ u(0) = u_0 \end{cases}\label{1}\tag{1} $$ When $A$ is an $M$-accretive operator it is known [1] that, a solution $u(t)$ can be given by an exponential formula : $$ u(t) = \lim\limits_{n \rightarrow \infty} \left[\left(I + \frac{t}{n}\right)^{-1}\right]^n u_0 \label{2}\tag{2} $$ which can be seen as an implicit Euler discretization scheme in time for the Cauchy problem \eqref{1}.
Question:
Is it possible for some operators $A$ (typically a laplacian) to approximate the semigroup using an explicit scheme such as
$$
U_{k+1} = U_k + hAU_k\;?\label{3}\tag{3}
$$
Reference
[1] Haïm Brezis "Analyse fonctionnelle et applications", Masson et Cie.