@Markiyan Hirnyk I show that erf(10.) is the source of the problem and that the erroneous value is exactly 100*sqrt(Pi). I also show the value of using exact arithmetic from the very start.

@acer In particular, you've changed the range of r from 2.5..4 to 0..0.4 and the range of x from 0..1 to 0..2. How did you know exactly how to change them?

@emmantop Your file didn't upload properly. Can you try uploading again?

Maple is saying that you need two more initial conditions. Can you come up with two more?

@ctnaz Your code contains this line, which makes no sense to me:

F[k+2]:=( sum(F[r]"*F"[k-r],r=0..k)+sum(G[r]*G[k-r],r=0..k)+sum((k-r+1)*H[r]*F[k-r+1],r=0..k)+M*F[k])*k!/(k+2)!:

What is the "*F" supposed to mean?

@adel-00 The symbolic commands maximize and minimize won't work in this case because the function is given implicitly. On the other hand, the commands in the Optimization package work numerically and will accept constraints.

@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).