  In this paper, we explore the interior dynamics of neutral and charged black
holes in $f(R)$ gravity. We transform $f(R)$ gravity from the Jordan frame into
the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and
Reissner-Nordstr\"om geometries. In simulating scalar collapses in
Schwarzschild and Reissner-Nordstr\"om geometries, Kruskal and Kruskal-like
coordinates are used, respectively, with the presence of $f'$ and a physical
scalar field being taken into account. The dynamics in the vicinities of the
central singularity of a Schwarzschild black hole and of the inner horizon of a
Reissner-Nordstr\"om black hole is examined. Approximate analytic solutions for
different types of collapses are partially obtained. The scalar degree of
freedom $\phi$, transformed from $f'$, plays a similar role as a physical
scalar field in general relativity. Regarding the physical scalar field in
$f(R)$ case, when $d\phi/dt$ is negative (positive), the physical scalar field
is suppressed (magnified) by $\phi$, where $t$ is the coordinate time. For dark
energy $f(R)$ gravity, inside black holes, gravity can easily push $f'$ to $1$.
Consequently, the Ricci scalar $R$ becomes singular, and the numerical
simulation breaks down. This singularity problem can be avoided by adding an
$R^2$ term to the original $f(R)$ function, in which case an infinite Ricci
scalar is pushed to regions where $f'$ is also infinite. On the other hand, in
collapse for this combined model, a black hole, including a central
singularity, can be formed. Moreover, under certain initial conditions, $f'$
and $R$ can be pushed to infinity as the central singularity is approached.
Therefore, the classical singularity problem, which is present in general
relativity, remains in collapse for this combined model.
