@PhD_Wallyson Your boundary conditions involve numbers such as 1.422*10^4, 4.881*10^9, etc.  That's makes it impossible for me to verify their correctness.  Please write them symbolically in terms of the parameters as E, I, etc.  Then I will be able to track down the errors, if there are any.

See my previous comments on how to handle numerical values in Maple.

@PhD_Wallyson In my previous reply I noted the need to correct the interface conditions at the supports.  You need to make those corrections before you can compare the results with those of the FEM code.

As to handling the numerical constants, look at our correspondence here.  See how the calculations are carried out without numbers.  Numerical values are introduced through:

span_lengths := L[1]=3.5, L[2]=5.0, L[3]=21.5;
characteristic_equation_numeric := eval(characteristic_equation, {span_lengths});

Do you see how that is done?

@Test007 Specifying the basis is the hard part and it varies greatly from one application to the next.  Do you have something specific in mind?

Once you have the basis, calculating the generalized Fourier series does not require any specialized tools.  You just define the Fourier coefficients through

a[n] = int(f(x)*phi[n](x), x=0..L);   # assuming one dimensional interval (0,L)

and then f(x) is expressed as

f(x) = Sum(a[n]*phi[n](x), n=1..infinity);

That's all.

@janhardo Okay, I believe that you have spent more than 5 minutes on your calculations., but as I said, you must have made an error.  Redo the calculations.

@janhardo The area of the the rectangle SJIK is (12/5)^2*8 = 1152 / 25.  The green area equals that minus 8, that is,  1152 / 25 - 8 = 952 / 25 = 38.08.  If you are getting something different, then you must have an error in your calculations.

@Carl Love Your ZigZag and ZigZagInv procs are quite clever.  I converted the first one from Reply to Answer in order to give it a thumbs up.  I don't know how to rearrange the followups into a proper sequence. If you (or anyone else) know how to rearrange, please do so.

@Carl Love That's excellent.  I had a feeling that the code can be shortened, but did not expect it to such an extent.

What is δ?  Is it a multiplier or a function?  At places you have δ(T−t)).  No space after δ indicates a function application.  At some other places you have δ (T−t).  A space after δ indicates multiplication. You want one or the other.

I haven't looked closely at the rest of your worksheet.  Make sure that you have no other similar issues.

If you continue having such problems, consider configuring your Maple for 1D input where issues like this don't arise.

@Jak Okay, that's better, but your question is unclear.

You say "I have two curves" but what you have shown are two expressions (not equations) which you have called eq1 and eq2.

One way I can think of making sense of "I have two curves", is to assume that your curves are given as eq1=0 and eq2=0.  Is that what you mean?

But in that case, eq1 < eq2 makes no sense since both eq1 and eq2 are zero.  I don't know where to go from here.

Perhaps you mean something else.  If so, then clarify.

In eq2 you have x[e(holling)].  What is it?

@vv That works better than what I could have imagined.   Thanks!.

@Test007 I did haven't changed any settings.  What I have shown is based on the version of OrthogonalExpansions dated May 27, 2016 from the site that you have noted, and run on Maple 2020.  How is your result different from mine?

@Neel 

@Carl Love A very nice construction.  Vote up!

@Carl Love Not related to the programming language per se, but to the worksheet interface: High on my wish list is some construct that would limit the scope of identifiers to a specified region of a worksheet.  Something like

scope
x := 12;
...
one or more execution groups here

end scope;

where the assignment x:=12 is effective only within that scope.

Admittedly, something like this can be accomplished through a proc, but that would hide the output of the individual statements within the scope.