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+//Eg-11.9

+//pg-488

+

+clear

+clc

+

+a = 0;

+b = 2;

+h = b-a;

+

+deff('out = func(in)','out = exp(-in^2)')

+

+//From equations [30],[31],[32] & [33]

+

+//Please note that the subscripts(i&j) we use here are different from that used in 

+//text book i.e they are increased by 1, because we cant give the index zero in   //scilab. Therefore,

+

+//Note : To get the results as in the book the lower limit of integration should be zero instead of 1 as in the book.

+

+imax = 6;

+jmax = 6;

+

+I(1,1) = h/2*(func(a) + func(b));

+

+I(2,1) = 1/2*(I(1,1) + h*func(a+h/2));

+

+I(3,1) = 1/2*(I(2,1) + h/2*(func(a+h/4) + func(a+3*h/4)));

+

+//From equation [33]

+

+sum1 = 0;

+

+for(j = 1:2:(2^3-1))    //Since we have to consider the odd terms only.

+    sum1 = sum1 + func(a+j*h/2^3);

+end

+

+

+I(4,1) = 1/2*(I(3,1) + h/2^2*sum1);

+

+//Similarly

+

+sum2 = 0;

+

+for(j = 1:2:(2^4-1))

+    sum2 = sum2 + func(a+j*h/2^4);

+end

+

+I(5,1) = 1/2*(I(4,1) + h/2^3*sum2);

+

+for(j = 2:5)

+    for(i = 1:imax-j)

+        I(i,j) = (4^(j-1)*I(i+1,j-1) - I(i,j-1))/(4^(j-1)-1);

+    end

+end

+

+printf(' The complete Romberg tableau is as follows\n')

+

+disp(I)

+

+printf('\n  Therefore, the value of the integral is %f\n',I(1,5))

+