>It is indeed close to the Mathieu equation. The intent is to demonstrate how a wave equation when modified can produce a frequency modulation. The mechanism behind sloshing is that not only can the forcing function

now you are talking again about sloshing, while the previous discussion was about electric circuits. Just to make it clear - I don't want to deny that the Mathieu equation describes some type of movement, which could eventually be seen as some kind of oscillatory behaviour - finally as said a trivial special case of the Mathieu equation is the simple oscillator. The question is however how exactly are these "movements" connected and I tried to explain that I don't see a closeness of this above Ansatz of "L-variable linear capacitor circuits" with the Mathieu Equation. Where at this point one should remark that it is not clear wether the ansatz that one can extend $ i(t) = C \frac{dV}{dt} $ in this way as outlined above is realistic.

Anyways I don't have the time to study articles in fluid dynamics, I just glanced at the paper you cited above and pinpointed the words

>The method applied to solve the system of Eqs...is the ETUDE finite difference method described in detail by Valentine ...

which gave me some frowns, as applying finite difference methods to nonlinear equations (and they talk about Bousinesq equations etc.) might not be appropriate. But as said I only glanced at the paper i.e. I even couldn't see in their not easy to read notation wether they actually apply that method. I just wanted to warn you, since I don't know how familiar you are with the discretization of nonlinear equations.