@Kitonum Vote up for finding a way to use map, however cumbersome.

@ogunmiloro The solution shown in your most recently attached file is garbage, and it has a very large error, 10^12, which comes from you trapping the "cannot evaluate" error. Like I said before, you can avoid this error by including the option maxfun= -1 in the dsolve command.

If you want to plot C(T) for any given assignment of parameter values, do

res(parameters= [...parameter values...]):
plots:-odeplot(res, [T, C(T)], T= 0..times[-1]);

One thing that might help is for you to provide a small range of feasible values for each parameter.

@mthkvv I'll take a look at this. I don't understand the first input of the norm algorithm. Please give details and show an example of appropriate input. In particular, I don't understand "unit" or the significance of theta, which doesn't otherwise appear in the algorithm.

@mmcdara But how do you get tasklist to show it instead of showing N/A?

@nm The grey box can be edited inline. There's no need to repeat the process to edit it.

@ogunmiloro You say that you've adjusted the code, but I still see times[1], not times[i]. I also don't see any warning message. I think that you attached an old copy of the worksheet.

@nm Please confirm for me whether the above Reply is true, i.e., whether only the restart is needed.

@nm Put the command that sets your libname in your initialization file.

@Reshu Gupta @Rouben Rostamian  I don't fault Rouben for not having spotted this for two reasons: It's a very unexpectedly simple ODE, and I only discovered this by an exceptionally patient reading of your input. Of course, if one had expected this simple form, it would've been trivial to get Maple to confirm it.

@ogunmiloro This error is because in two places in the ODEs, you've used b[o] where you should've used b.

Several questions:

1. The data C__f strongly suggest that C(0) = 1. So why do your ICs have C(0) = 400? Do the other ICs also need to be rescaled accordingly?
2. Why don't you use the full data set C__f (153 values)?
3. Using your initial parameter values, C is an oscillatory function with a horizontal asymptote. That doesn't fit C__f at all. C__f looks like an exponential function.
4. Should times start at 0 rather than 5?

Hints:

1. As Tom Leslie pointed out, times[1] needs to be times[i].
2. Add option maxfun= -1 to the dsolve command. This will eliminate most (perhaps all) of the "cannot evaluate" errors.

An exponential function fits C__f very well. This is shown by

Statistics:-ExponentialFit([$1..nops(C__f)], C__f, T, summarize);
Summary:
----------------
Model: 6.2601204*exp(.70239574e-1*T)
----------------
Coefficients:
              Estimate  Std. Error  t-value   P(>|t|)
Parameter 1    1.8342    0.1961      9.3532    0.0000
Parameter 2    0.0702    0.0022      31.7944   0.0000
----------------
R-squared: 0.9774, Adjusted R-squared: 0.9771

@mmcdara I've made progress on Windows 10 with your tasklist suggestion. The process identifier is returned by kernelopts(pid), so I get the one line for the current process (9040 in this example) like this:

StringTools:-Trim(
    ssystem(
        sprintf("tasklist /fi \"PID eq %d\" /v /nh", kernelopts(pid))
    )[2]
);
"mserver.exe 9040 Console 1 141,528 K Unknown DESKTOP-IL8TQTN\carlj 0:20:54 N/A"
[I hand-trimmed excessive internal whitespace from this output.]

The last field, shown as N/A, is the Window Title. I guess that's the value that we want filled in?

@Carl Love Actually, just doing a restart (and nothing else) in worksheet A may be enough.

@emendes The settings of infolvel[...] trigger the execution of the userinfo statements in the code. The number of these statements to include is up to the command's author.

@emendes It only makes sense to me to change the outer seq to Grid:-Seq.

I don't see much hope for a useful solution. You're attempting a nonlinear fit of 15 parameters with only 20 data points. On top of that, the 20 dependent-variable values have only 4 distinct values.