A code to defined for the havlving for the trapezoidal rule

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.

Thank you in advance

Answer 1

[Chidvi Modala]

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