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The essential point to take away is that with models formulated using (3) the charge must be estimated from the capacitance. There are different ways of doing the estimation. The backward Euler approximation given above estimates the change in charge from the capacitance at the end of the step; forward Euler uses the capacitance at the beginning of the step, and trapezoidal rule uses a combination. Each produces an error that grows with the time step that causes charge to not be conserved. With models formulated using (2) the charge is computed explicitly, so there is no approximation.
TRAPezoidal numerical method has no damping and will
often be seen to "sawtooth" between upper and lower
tolerance limits. This, with any subsequent gain, can
make for unrealistic behaviors in the circuit, a transient
noise of sorts with consequences TBD.
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