@Simon45 

Your code solves directly the problem using a "big" linear sistem in the unknowns y[k,j].
As I see you have the task to solve it using a sequence of tridiagonal linear "smaller" systems.
These methods are standard. You must look in your textbook or lecture notes and see how the equations can be arranged.
Or, you may google for "heat equation discretization".

@Rouben Rostamian  

After posting the solution I have also found Kurtz' article.
Note that "=" also can be used to find a simple sequence (with smaller 1/a[n]) namely:
a[n] = 2^( - n*(n - 1) ), n>0,  a[0]=1/2.

subsop(2=s,J)

replaces the second operand of J (which is  s = xi1 .. L1)  with   s.

See in the help file:
?subsop

@digerdiga

@mimi990 

fun11 is actually a vector (of dimension 1) containing the integral. So, fun11[1]  is the integral itself.
The subsop converts the definite integral into an indefinite one.

@9009134 

This function is also non-periodic. 

In general, if two continuous nonconstant periodic functions f, g : R --> R have incommensurable periods (i.e. their ratio is irrational) then f + g is non-periodic.

I don't know what you mean by minimal period in this case; d is not periodic. The periods of the two terms are incommensurable, there is no common period.

@Kitonum 

It's impossible to get uniform approximations this way. E.g. for t=40800*Pi..40800*Pi+3  the difference is very large.

@mmcdara 

This is another function. OP says f(t)=t^2 for t in [0,2*Pi]. It has discontinuous periodic extension.
Yours is continuous.

@mmcdara 

Sorry, but you are confusing "Fourier series" with "Fourier transform".

@mmcdara 

But sum(1/u, u in L) is nonsense in Maple (just try it for L:=[1,2]). Any such nonsense will produce infinity due to the empty catch clause. I think that you meant add instead.

@mmcdara 

The standard periodic extension of a function f defined in [0,T) is simply x |--> f(x - floor(x/T)*T).
It's not about distributions here. In the theory of Fourier series, the integrability is in [0,T). I think that you have in mind the Fourier transform.

@Zeineb 

Have you checked for all b?

@tomleslie 

Nice, vote-up!
I'd suggest to insert in your code

nE,nV := NumberOfEdges(T), NumberOfVertices(T);
# Produce all subgraphs of G which have the same number of edges and vertices as the "test" sub-graph T
U:=choose(Edges(G),nE): nops(%);
U1:=select(t -> (nops(`union`(t[]))=nV), U): nops(%);
gL:= Graph~(U1): nops(%);

in order to reduce the number of candidates.
 

@Carl Love 

The Squeezing Theorem cannot be used here.
If   limit(liminf(f(x,y), y=0), x=0)  and  limit(limsup(f(x,y), y=0), x=0)  exist and are equal,
it does not imply the existence of limit( limit(f(x,y), y=0), x=0); and actually it does not exist.

BTW, it would be nice to have liminf and limsup in Maple.

@acer 

A very nice and professional patch (a single line of code added). I hope to be included in the next Maple update.