@Markiyan Hirnyk Oh, I missed that. You're right. Sorry.

@Markiyan Hirnyk The point returned by Optimization:-Maximize does not correspond with the local maximum shown on the graph. The point returned by Minimize looks okay.

Could you please attach a worksheet with your code?

@ctnaz Sorry, I don't know anything about the Differential Transform Method (DTM). Hopefully someone else can help you. Also, I don't understand what Pr(theta~) and f*theta mean. And what is gamma? I doubt that you mean the constant gamma.

@candy898 Hmm. I don't understand why it's not working for you. Try

 p := LinearAlgebra:-LinearSolve(LinearAlgebra:-IdentityMatrix(2)-C, d);

I wonder if this is a 2d-input issue.

Can you show your exact Maple session? Note that Matrix is spelled with a capital M in Maple. And LinearSolve has a capital L and S. (And it is not "slove"!)

It worked for me when I spelled things correctly. However, I don't think that that is the way to solve the closed-economy Leontief model. (I-C) is singular in this case. I think that you need an eigenvector of C corresponding to eigenvalue 1.

@candy898 You did not execute the first line of my worksheet:

macro(LA= LinearAlgebra);

@Preben Alsholm I was able to do N=40, but not N=50.

Regarding the second problem, see the Wikipedia article "Smallest circle problem". According to that, there is a linear-time (linear in the number of vertices) algorithm for a much larger problem: any number of dimensions, and any finite set of points (not necessarily convex or a polygon).

Would you please post an example of this?

@Gaia 1. When you get that message "Length of output exceeds 0 ...", the computation is still performed; it is just not displayed on screen. It is possible to increase this limit, but do your really want to see such a large output?

2. Maple is used in distributed processing. The Grid package facilitates this. See ?Grid .

@Gaia Sorry, I was wrong: nextperm, etc., will not work with restricted size permutations. There are two other permutation iterators that will work.

Method 1: package combstruct

with(combstruct):
list6:= convert(list5, list):
Iter:= iterstructs(Permutation(list6), size=2):
while not Iter[finished] do
     p:= Iter[nextvalue]()
end do:

Method 2: package Iterator

You'll need to download Iterator from the Maple Applications Center. And I think that it requires Maple 17. It definitely requires Maple 16 or greater.

for p in Iterator:-Permute(list6, 2, compile= false) do
     print(p)
end do;

@bails123 For the plot, you make a simple change to relabel the horizontal axis as z/b, with the range being 0..1:

plot([seq(BesselJ(0, BesselJZeros(0,n)*sqrt(`z/b`)), n= 1..4)], `z/b`= 0..1);

You wrote: For the animation, since I cannot obtain values for K[n], I was thinking I could plot y_n(z,t)/K[n] as a function of t.

Hmm. I don't see how that's different from setting K[n] = 1, which is what I did.

You wrote: Sorry, I should have been more clear, it was an animation as a function of t.

So, you want the horizontal axis to be t and the animation variable z?

@stevens1111 You are missing a multiplication sign in your definition of P(z).

@mbacon29 Your fourth initial conditions have x*0 where it should be x(0).