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//Example 14.5
//Romberg Method
//Page no. 457
clc;close;clear;
deff('y=f(x)','y=1/(1+x)')
h=[0.5,0.25,0.125]
for k=1:3
for i=0:h(k):1
x(i/h(k)+1)=i;
y(i/h(k)+1)=f(x(i/h(k)+1))
end
n=1+(1/h(k))
//trapezoidal rule
S=0;
for i=1:n
if(i==1 | i==n)
S=S+y(i)
else
S=S+2*y(i)
end
end
S=S*h(k)/2
printf('\n\nI(%g) = %g',h(k),S)
z(2*k-1,1)=S
end
for i=2:3
for k=1:4-i
z(k*2+i-2,i)=z(2*k-1+i,i-1)+(z(2*k-1+i,i-1)-z(2*k-3+i,i-1))/3
end
end
printf('\n\n')
disp(z,'The Table of values:')
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