Convergence on components containing 'if' function or conditional expression

[GszaboLuther]

If I create a component model which contains 'if' function or conditional expression usually I get a convergence issue.

For instance if the component contains

B1 out 0 V = { if (V(1,2) > 0, 1, -1) }

or

B1 out 0 V = { V(1,2) > 0 ? 1 : -1 }

the convergence is problematic near that point where the V(1,2) goes through 0 because the function of B1 has a discontinuity at 0. As a mathematician I understand that the simulation of such a behavior is problematic.

My questions are:

1. If the simulation can't be convergent for these types of expressions why they are among the resources?

2. If the simulation is possible how to set up the simulation for that circuits which contain such components?

3. If the simulation is possible only for some circuits of special type what they are?

[GszaboLuther]

For the first question I have already know the answer:

With help of the 'if' or the conditional expression I can create also a function which has no discontinuity but has some breakpoints. And the breakpoints don't cause convergence problems. 

[tipa]

Здравствуйте! Всё это очень интересно, но хорошо бы примеры привести симуляций, а не пальцами в воздухе крутить...
С уважением...