calculate the error of an integral from two, 2 column data sets using repeat simpsons rule in matlab in matlab

main.m
% Load data sets
x = [ ... ];
y = [ ... ];

% Use the trapezoidal rule to estimate the integral
trapz_integral = trapz(x, y);

% Implement the repeated Simpson's rule
N = length(x) - 1; % Number of subintervals
a = x(1); % Lower limit
b = x(end); % Upper limit
h = (b-a)/N; % Interval width

% Evaluate the integrand at each sample point
y0 = y(1);
yN = y(end);
y_odd = y(2:2:end-1);
y_even = y(3:2:end-2);

% Apply the Simpson's rule formula
S = h/3 * (y0 + yN + 4*sum(y_odd) + 2*sum(y_even));

% Use the difference between the Simpson's rule estimate and the trapezoidal rule estimate as an estimate of the error.
error_estimate = abs(S - trapz_integral);
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