Good code. Well, at least in terms of the documentation. Excellent in that respect. Readable code is important when you need to debug it. It is also important if you get run down by the crosstown bus, and your colleague needs to use your code. So well done in that respect.
You did not return all of the outputs you listed. But my guess is, you were not done writing it, because you found a problem. The lack of semi-colons on some lines tells me you were not done, and were debugging your code. For that though, LEARN TO USE THE DEBUGGER!
One obvious problem lies at this line:
elseif Mid2 == 0
Surely you wanted to know if func(Mid2) is zero, NOT if Mid2 is zero.
Anyway, I think your problem lies in confusion about the endpoints of the interval. They need to change as necessary. Xl and Xu are not going to be constant. Let me give an example. I'll use bisection to determine the root of
F = @(x) 3*x - 2;
And yes, I'll bet you will guess it happens at x==2/3==0.6666666666... But let me try bisection. I'll set the initial interval of interest as [0,1]. Clearly that brackets a root, since there is a sign change between the endpoints.
Xbounds = [0,1];
Fbounds = F(Xbounds)
Xmid = mean(Xbounds)
fmid = F(Xmid)
Now what is the new interval? We choose the endpoint that will show a sign change from Fmid.
Xbounds = [Xmid,Xbounds(2)]
F(Xbounds)
Now, we start a new iteration.
Xmid = mean(Xbounds),Fmid = F(Xmid)
And here, it is the LOWER bound that we will keep. Replace the upper bound with Xmid.
Xbounds = [Xbounds(1),Xmid]
I hope you also see we are getting closer to x = 2/3 as the solution. One more iteration may help.
F(Xbounds),Xmid = mean(Xbounds),Fmid = F(Xmid)
Xbounds = [Xmid,Xbounds(2)]
Now, go back, and look at your code. Your code never updates the interval for bisection. It keeps Xu and Xl as unchanged.
Do you need to change your code to look like what I wrote? Well, I think my version is cleaner, by using the variable Xbounds as always the interval of interest, that brackets the root. It means I have fewer variables to keep track of, and that is ALWAYS a good thing. Regardless of what code you do write, you need to look at my example, and see how it tracks the root, updating the lower of upper endpoints of the bracket as necessary. That is the crucial part.
