Question

Give me a MATLAB code which integrates any function using Romberg integration

The code must work fine or else I will down vote the answer badly

Dont post if you dont know

Answer 1

The given MATLAB CODE takes any function and integrates it as per the rule of Romberg as per various levels and prints the result. The intermediate trapezoidal rule code is also shown

The sample is shown for f(x)=1/(1+x) for 5 levels from 0 to 1

clc;clear all
format long
f=@(x) 1./(1+x);
a=0;b=1;h=1;n=5;
ans1=RombergIntegration(f,a,b,h,5);
fprintf('Desired answer is %5.6f \n',ans1(1,n+1))
function I=RombergIntegration(f,a,b,s,level)
for(j=1:(level+1))
ni=s*2^(j-1);
I(j,1)=trapezoidal(f,a,b,ni);
end
for(j=2:level+1)
for(k=1:(level-j+2))
I(k,j)=(4^(j-1)*I(k+1,j-1)-I(k,j-1))/(4^(j-1)-1);
end
end
end
function answer=trapezoidal(f,a,b,n)
i(1)=f(a); i(n+1)=f(b);
h=(b-a)/n;
x=a:h:b;
i(2:n)=2*f(x(2:(length(x)-1)));
answer=0.5*h*sum(i);
end