Try this. There were a few issues with the abs(R(i,i)-R(i-1,i-1))
condition for the while
loop.
function [R] = romberg(f,a,b,delta,nmax)
R=zeros(nmax,nmax);
R(1,1)=(f(a)+f(b))*(b-a)/2;
i=2;
E=2*delta;
while i<nmax && E>delta
m=2^(i-1);
R(i,1)=trapez(f,a,b,m);
for j=2:i
R(i,j)=R(i,j-1)+(R(i,j-1)-R(i-1,j-1))/(4^j-1);
end
E=abs(R(i,i)-R(i-1,i-1));
i=i+1;
end