For a real diode, the current is very small (in the order of $uA$, but not zero) when the voltage is applied in reversed direction.
It means that the resistance of the diode is very large, but it is not infinite.

When the voltage is applied in forward direction, the result will be similar to standard RLC circuit ($V_V+V_R+V_C+0.8=0$).
However, when the voltage in in reversed direction, the change of the current will be limited by inductor, most of the voltage will be across the diode and the resistor. I will need to know the resistnce of the diode in order to calculate the voltage across the inductor.
i.e. $V_L= - (V_C+V_R+I*R_{diode})$. I need this value to calculate $T(t+dt)$ from $\frac{dI}{dt}= -V_L/L$