# A code to defined for the havlving for the trapezoidal rule

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Mark Loui on 26 Mar 2021
Answered: Chidvi Modala on 31 Mar 2021
Hi i like to ask is there a version of the codes which enables me to find the xnew in the halving for the xnew in the Romberg integration or
basically, if there is a line where a is the first point =0 and b is the end point=1; and h=b-a
I like to find is this xnew is to find for the xnew to be changing by half every loop
for example
for i=1:n
h=h/2; %Halfing the h for each new loop
xnew=a+i*h %To get the xnew every loop, but the problem i face here is how to get for the x new to be added into a vector form where the xnew values is also changing for each of the loop where the loop is filling with the xnew values in a vector form at the current loop.
another explaination is
for 1st iterations
h=h/2
xnew=a+h*1 which is also equals to xnew=0.5
for the 2nd Iterations
h=h/2 which is now =0.25 as the h was 0.5 from the previous loop
xnew =a+i*h, the problem i face here is that there should be two new values which are xnew =0.25 and 0.75
for the 3th iterations
h=h/2
xnew has to be equal to 0.125, 0.375, 0.625 and 0.875
and the loop goes on
to stop the loop let says as simple as just
err=0.1;
tol=0.01;
while err>tol
h=h/2 %we can use a for loop if it helps
xnew values
err=err-0.01;
end
This while loop is just keep the loop running as i want to find how many loops it required to reach for the err to be smaller than the tol, and what i also want is the xnew values at that iterations.

Chidvi Modala on 31 Mar 2021
You can make use of struct datatype. You may refer to the following code:
b=1;
a=0;
n = 100;
s = struct('xnew',0, 'h', b-a);
err = 0.1;
for i=1:n
if i==1
s.h(i) = (b-a)/2;
else
s.h(i)=s.h(i-1)/2;
end
s.xnew(1:i) = a+i.*(s.h(1:i));
err = err-0.01;
if err<0.01
index = i;
break;
end
end