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

To calculate the error of an integral from two column data sets using the repeated Simpsons rule in MATLAB, you can follow these steps:

  1. Load your data sets into MATLAB, and store them in matrices x and y.
  2. Use the trapz function to estimate the integral using trapezoidal rule.
  3. Implement the repeated Simpson's rule by applying the trapezoidal rule on alternate subintervals.
  4. Use the difference between the Simpson's rule estimate and the trapezoidal rule estimate as an estimate of the error.

Here’s the code:

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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Note that the accuracy of the error estimate will depend on the smoothness of the integrand.

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