initial commit / add all books

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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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