Contents
Example 3.2
Romberg integration
format long;
I_1, I_2, I_3, I_4
I = zeros(4,1); h = zeros(4,1); for i = [1:4] N = 2^i; h(i) = (pi-1)/N; X = [1:h(i):pi]; f = sin(X)./(2*X.^3); for j = [2:N] I(i) = I(i) + f(j); end; I(i) = I(i) + 1/2 * (f(N+1) + f(1)); I(i) = I(i)*h(i); end;
I_12, I_23, I_24
I_12 = (4*I(2)-I(1))/3; I_23 = (4*I(3)-I(2))/3; I_34 = (4*I(4)-I(3))/3;
I_123, I_234
I_123 = (16*I_23-I_12)/15; I_234 = (16*I_34-I_23)/15;
I_1234
I_1234 = (64*I_234-I_123)/63
I_1234 = 0.198558772329654