@sarra The file link is working now.  I see what you mean. The functions appear different for the 5th, 9th, 10th, and 11th values of t. I think that the 5th is normal acceptable variation. But the numerical solution seems to become unstable starting at the 9th value of t. By the 11th value, it appears to be chaotic. I don't know why this happens, and I don't know much about finite-difference methods. For what it's worth, I set the numeric solution to be computed to 100 Digits and it did not change the situation. I know that certain finite-difference methods are inherently unstable under certain conditions related to the relative values of the spatial spacing h and the time spacing k; I don't remember the exact formula. What is the precise name of the finite-difference method that you are using?

@sarra Please try uploading the file again.

The last sum that you give is just the very well known sum of a geometric series:

sum(1/n^x, x= 1..infinity);

Then the nested sum is just a slight variation of the well known

sum((-1)^n/(n-1), n= 2..infinity);

@mehdi jafari You are using indexed variables (a[0], a[1], etc.) in your Answer, whereas the OP is using concatenated variables (a0, a1, etc.) in the Question. While you may argue that indexed variables are better, the distinction should at least be noted.

You haven't defined A anywhere in the problem statement. The only thing that makes sense to me is that A is an N x N matrix. But the stated convergence property would only be true for certain A, those with spectral radius less than 1.

@hillyzz Copying the code is fine, but it is incomplete. I need the values of k_min, k_max, n0, n1, and n2. Also, what is the procedure multiply? Do you just mean to multiply the Matrices? That can be done as P1p.F1p.P2p.F2p.

@DJJerome1976 For some values of theta, filled is interpretted as the area between the curve and the x axis. It ignores the fact that it is polar coordinates.

@Preben Alsholm It seems that the option filled= true doesn't do anything when used with animatecurve.

Please do not edit a Question, making substantial changes, after the Question has been Answered! If you do, then the Answers don't make sense.

The original question was to find the Fourier series for x^2 on -Pi..Pi and to evaluate this at x= Pi to prove that Sum(1/n^2, n= 1..infinity) = Pi^2/6.

@mahmood180 

Mahmood,

Please note my correction to Mehdi's Answer. You need to change nops(C) to numelems(C). The nops is only using the first three of the five constraints. This causes a small change in the final answer.

Please post a more-detailed example. Certainly the information can be extracted from the plot data, if need be. Generally (there are some exceptions), one can extract the data matrix from a plot like this:

plot(...);
P:= %:
M:= op([1,1], P);

Then M is a matrix of two columns, the first being the x values and the second being the y values.

More sophisticated solving techniques may be possible also.

@mehdi jafari

Mehdi,

You correctly indentified the source of the error as the {C=0} in the line

However, your correction

is not quite correct. You cannot correctly apply nops to a Vector. You need to use numelems instead. nops(C) returns 3, whereas the correct number of elements is 5. This makes a small change in the optimal point.

@acer It doesn't work for me. I get this error message:

Error, (in dsolve/numeric/SC/preproc) unable to compile (rc=1), please try again, and if that fails verify your Windows compiler installation

I am using the default Maple 18 compiler, which seems to work for me in other cases.

Using Maple 18/64 on Windows 8.1/64.

Does the compile option work for you on this ODE system?

@J4James Where did you get that piecewise expression? I don't think that you can use that. As far as I can tell, this sum is not the Fourier series of a piecewise constant function. As far as I can tell, it is the Fourier series of 2*ln((1+sin(2*Pi*x))/(1-sin(2*Pi*x))).

@victormath19 You need to re-execute the code. The execution of the dsolve and the animation command must be in the same "session". When you re-open a worksheet, the results of prior computations are not accessible, even though they may be displayed.