I've been thinking about this and I see how you can construct the integrated system of equations directly. However, I don't see how you get from there to a smaller non-linear system of equations?mystran wrote: ↑Tue Nov 10, 2020 12:11 pmMy experience doesn't mirror this, but maybe I'm missing something. The idea with the trapezoidal is that in the fixed time-step case one can rearrange it into a TDF2 form, which then only needs a single combined delay, which means one can put the whole thing into the MNA matrix and solve for the new state directly, skipping the separate integration step. In contrast, with pretty much any other rule (well, other than Euler) you either need extra dimensions or a separate integration step.

This is not profitable if you want a full solution of all the nodes (because now you need extra work to decode the voltage over your capacitors), but it is profitable when doing a real-time solution from inputs to outputs only.

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What I've always done is just design component stamps directly in such a way that no symbolic manipulation is necessary and dimensions can be directly tagged based on the evaluation stage requestion (eg. linear, varying, iterated), then do a purely numerical solution.

After stamping out a matrix with MNA component stamps, the non-linear equations will depend on other parts of the circuit, and can't be solved by themselves I don't think? Or maybe I'm missing something? It would be funny if so, I spent quite a lot of time and effort on my current approach because I couldn't find a simpler way...