Using the RK4 VI, had a question about implementation

Question

Here's a link to the system I'm approximating:http://i.imgur.com/EXnswBm.png
The way it's going to be used, it will use current values to calculate values that will be important in the next iteration of a while loop. The values passed into it via the X0 input will be from the last loop iterate, and the values coming out will be sent into a shift register. The length of each iteration varies according to another VI, so it'll be flipping between 5 and 10 minute cycles.
My question pertains to that max[] that's in the DE for I1(t).
Since labview isn't a functional language, I know that whatever I put into the F(X,t) array will be interpreted as a string, and not parsed as a function. Since the max operates on one of the variables, I can't simply apply the max[] operation outside and just leave that space as a number, or a dummy variable.
So is there any way to do this? Even a case structure wouldn't handle it, because it'd have to be applied for every iteration of RK4, and not just to the VI as a whole

Answer 1

The fundamental issue is that max() is not a differentiable function so the system of equations is not one which RK would be expected to solve.  Any differential equation solver in LabVIEW or a text-based language will need to do something beyond the normal solving process to deal with the discontinuities created by max().
If I2 is reasonably well behaved near zero, creating two sets of equations for I2 > 0 and I2 < 0 and switching based on the previous value of I2 might work.  It will be much slower because you will need to stop and start the solution process.
The RK algorithms are documented in a number of references. It might not be too difficult to program your own with the max() function built in.
Lynn
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