Richardson extrapolation for Simpson's rule -code matlab

I need you to help me with the code for the Richardson extrapolation for Simpson's rule

Does anyone could help me with this code please?

Answer 1

[bym]

Simpson's rule is a Richardson extrapolation of the trapezoidal rule, the following should get you started:

clc;clear

yLow = sin(0:pi/10:pi);
yHigh = sin(0:pi/20:pi);
iL = pi/10*trapz(yLow);
iH = pi/20*trapz(yHigh);
format long
re = (4*iH-iL)/3; % Richardson extrapolation

err = [iL (iL-2)/2; ...
       iH (iH-2)/2; ...
       re (re-2)/2];
fprintf('Estimate\t\terror\n')
fprintf('%1.10f\t%1.10f\n',err')

Estimate    error
1.9835235375  -0.0082382312
1.9958859727  -0.0020570136
2.0000067844  0.0000033922