@nm Include the discont option in the plot.

@Bendesarts wrote:

The system is a ODE with 15 parameters and many trigonometric function for the coefficients. It's big but for a a mechanical system a bit complex is not huge.

One point which makes the system looks like very big comes from the fact that i have copy the matrix with copy/paste for my code where i have applied machanical theorem so as to obtain the equations. When you do like this, the copied matrix are good but they looks likes with a strange form which takes a lot of place.

My assessment of the size of the system is based purely on the length command and not on the visual appearance of your matrices. The length of 2 Gig means that if the system were printed out, it would be nearly 1,000,000 pages long. The complicated expressions are the result of the inversion of 12 x 12 symbolic matrices.

I have a feeling that there is some way to solve the differential system first and then invert numeric matrices. But I don't know exactly how to do it.

I notice that problem 2 is now fixed. I haven't checked #4.

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@Deltafee Please upload your worksheet so that I can diagnose the problem. Here's my doing of it:

Download NonlinearFit.mw

Your system is so large that I don't think that there's much hope for dsolve being able to handle it. The size of sys as measured by length({sys}) is over 2 Gig. That's so large that the length command itself takes several seconds to finish.

@acer How much of the computation of evalf(3/Pi, 1) is done in evalhf? Is it just the numeric evaluation of Pi?

@ecterrab My opinion is that it is an improvement---above and beyond the call of duty.

@Deltafee It should be

sol[1]:= Statistics:-NonlinearFit(f, xlist, ylist, x);

This is only a partial explanation: Since Digits is less than 16, the computation evalf(3/Pi, 1) is done in hardware double precision (evalhf mode). This makes it harder to see what's going on, because the debugger shows nothing. That being said, I consider the 0.9 result a bug.

@danlun I was not suggesting that my code

(expand@@2)~(expr1);

was a means to simplify your expression. It was a side-comment only relevant to Markiyan's code.

@Christopher2222 "...powers of cos(x)...."

@nm Perhaps one can get a numeric solution from dsolve after converting to a differential equation (if the conversion is possible). Even for symbolic solution, dsolve can solve many nonlinear equations, and is much more powerful than intsolve.

@Markiyan Hirnyk wrote:

map(proc (c) options operator, arrow; expand(c) end proc, op(expr1)):
map(proc (c) options operator, arrow; expand(c) end proc, op(map(proc (c) options operator, arrow; expand(c) end proc, op(expr1))));

These steps are not valid transformations! The op causes a drop of all factors or terms other than the first. Indeed, your final answer is just the first term of the expansion of a subpart of the original expression. If you take out the ops, it is valid, and it is equivalent to simply

(expand@@2)~(expr1);

or

map(expand@@2, expr1);

I notice that problems 1 & 3 have been fixed today. I haven't had a chance to verify 2 & 4.

@Markiyan Hirnyk The source of the error is competely different in this question.