And I tested a few more cases and I found a trend that using Method Gear tends to use shorter time step, (which generates more points) and usually better results than Method Trap does. So can I say for a simulation with various time steps(we want the step to be as large as possible while maintaining the accuracy, so I set the maxStep to be a big number, (Tstop - Tstart)/20 instead of the default step given by the command) method Gear tends to use a more conservative step size than Method Trap does? Does anyone have literature/proof for my conjecture?
"For a fixed time step, the most accurate of these methods in a local sense is the trapezoidal rule, followed by Gear2. ... but the trapezoidal rule would typically allow larger time steps and so require a shorter run time. ...
thus it is not usually the best choice when reltol is loose."
First, I understand that it is hard to say the default reltol(1e-3) is tight or loose without having the circuit in hand, but I assume the default one for a full-chip setting is loose.
"The higher-order backward-difference formulas are efficient when tolerances are tight or when computing very smooth waveforms."
F(t) = Gear2 - Trap with the assumption that \[X^n, X^{n-1}\] are the same timept under 2 methods, aiming to check who has a bigger \[X^{n+1}\] under different assumption.