Not spotting where/how index exceeds number of array elements

I'm trying to solve a Navier-Stokes setup in a cylindrical coordinate system and am bumping up against an array indexing challenge. Any help folks might be able to offer to straighten matters out would be most appreciated. I'm including my live editor content below.

Answer 1

[Vladimir Sovkov]

Is this what you want? Live script vesion is attached.

xmesh = linspace(0.01,0.05,5);
solinit = bvpinit(xmesh, @guess);

sol = bvp4c(@bvpfcn, @bcfcn, solinit);

plot(sol.x, sol.y, '-o')


function bound = bcfcn(ua,ub)
bound = [ua(1)-0.1, ub(1)];
end

function g = guess(r)
g = [1*(0.05-r)/(0.05-0.01), -1/(0.05-0.01)];
end

function dudr = bvpfcn(r,u)
dudr = [u(2), u(2)./r];
end

[Vladimir Sovkov]

If you want to see the solution u1 alone, replace

plot(sol.x, sol.y, '-o')

by something like

plot(sol.x, sol.y(1,:), '-o')

In my opinion, a thicker xmesh (e.g., 50 nodes in place of 5) would be more representative.

[Brian Taff]

Many thanks, Vladimir. Based on your feedback I am up and running. To provide an update for any subsequent readers, I'm attaching the revised and corrected content.

Yes, two issues:

1. An oversight on my part of the ./ operator and
2. A late realization that running of live .mlx scripts only executes the "section" of the report where you are located without some added caretaking.

[Vladimir Sovkov]

No prob.

I do not understand why you replace your initial equation by . It seems to me that must have been with the "plus" sign, and, consequently, dudr = [u(2), u(2)./r] in the program, isn't it? Otherwise, you are solving the equation .

[Brian Taff]

You are correct, I had mistyped the original equation in the live editor's documentation. It should have been stated as u'' + u'/r = 0.

The downstream function calls do, in fact, solve this equation and the results were as intended.