I've discovered that if one has convergence problems with the circuit simlation software LTspice, the option cshunt may give you some hope in resolving the issue. But, why exactly does adding small value capacitors helps with convergence?
I made another question relating to these concept here
If the self-resonant frequency of an inductor is ridiculously and unrealistically high due to lack of parallel capacitance and you do something to cause it to 'ring' the time step to simulate the ringing will be too small. If you look at real (and tiny) inductors, say 10nH, the SRF is perhaps 5GHz, so that implies 0.1pF of parallel capacitance exists.
In general if the parts are too ideal (resulting, say, in too high 'Q') you might have convergence problems. The algorithms also require smooth (differentiable) behavior. For this reason, switches that behave properly do not snap from \$\infty\$Ω to 0Ω, rather they smoothly change from a high resistance to a low resistance in a continuously differentiable curve.
In reality you're going to have significant capacitance in parallel with any inductance, certainly significant in comparison with numbers like 0.0001pF. LTspice also helpfully (?) can add some resistance in series with inductors (1mΩ by default), and has a convergence hack that optionally adds a minimum inductor damping if you omit a parallel resistor.
You could probably play with the Control Panel defaults and get it to converge with insanely non-physical numbers but that might not be desirable unless you are sure your numbers really have some resemblance to reality (there is a risk of getting results that are 'garbage-in garbage-out' rather than 'garbage-in warning out'). And even that won't save you if there is a zero value where there needs to be something non-zero.
