@vv Okay then. I hadn't previously noticed your corresponding change of the coefficients.

@adel-00 You spelled solve as "slove".

Assign the result of solve, for example

xyz:= solve(...);

Then in the plots, do

plot3d(eval(x, xyz[]), ...);

and likewise for the y and z plots.

@FDS Regarding efficiency, the time on my computer to compute the minimizing parameter values for the 192 data points was 120 milliseconds.

@vv You changed the 3rd modulus from 23^3 to 23^2. Apparently, this doesn't change the final x and y.

@FDS Okay, but note that my technique reduces the error (specifically sqrt(SSE), the square root of the sum of the squared residuals) by a factor of 26 compared with the MathCAD values.

Edit: I just saw that you increased the data points to 192. I'll make the comparison again with the new data.

Edit 2: Using the new data, my reduction factor in sqrt(SSE) is 1.4. The parameter values that I got are Q__0 = 7018.5, Q__s = 2813.2, k__f = 2.0578 * 10^(-5). These are in the same ballpark as the MathCAD values.

@Joe Riel kernelopts(bytesused) tells you how much memory has been used over the entire session (i.e., since restart) including memory that has been used multiple times. So, it's a non-decreasing value, and it isn't very relevant for someone who's running out of memory. What's needed is How much memory is currently being used? That's what the 3rd column of kernelopts(memusage) tells you.

MmaTranslator:-Mma:-MemoryInUse() returns the sum of that 3rd column, although it does it with the incredibly inefficient coding style that's typical of that package, making 64 separate calls to kernelopts(memusage) where 1 would suffice.

@Joe Riel I also find kernelopts(memusage) very useful for this. Matrix(kernelopts(memusage)) gives an easier-to-read presentation. The columns are

1- the type of kernel data structure
2- number of structures of that type
3- total bytes used for those structures

@Preben Alsholm Immediately after you (as Moderator/Editor) make the change, the edited item appears on your screen as any normal post or question. At that point, make a Reply. If you have nothing significant to say, you can simply say "I changed this from a Post to a Question." I think that making a Reply prevents the item from getting lost for several hours.

I changed this from a Post to a Question. 

@Prakash J The expressions D[t] and D[B] make no sense as differential operators. If these are meant to be parameters, then use a variable other than D.

@Preben Alsholm When a Post is changed to a Question, or vice versa, it usually disappears for several hours.

@philroe Your other Reply is missing.

@vv You wrote:

• Of course 2 is the "generic" value of the rank. The exact value is given by:
      ans:=(x,y) -> piecewise(x<>0 and y<>0, 2, x<>0 or y<>0, 1, 0)

Yes, if we consider the field of the original matrix to be the complex numbers C with x and y being parameters representing field elements, then that piecewise solution applies. On the other hand, if we consider the matrix's underlying field to be C(x,y) (rational functions in x and y with complex coefficients), then the generic rank is the rank. But no field can make the rank 3.

This recent Post may be helpful: "Who says Maple doesn't have dark mode?" Since the proposed solution uses Jupyter, I don't know whether it'll be useful to you.

@Carl Love I think @dharr 's simple Answer is probably better, unless perhaps you want to remove the parentheses from the numbers.