% Function for Romberg integration method
% Computes the integral of a given function using Romberg's method
% Renamed function: romberg_integration
function [R, quad, e, hr] = romberg_integration(func, a, b, n, toler)
mr = 1;
hr = b - a;
e = 1;
j = 0;
R = zeros(4, 4);
R(1, 1) = h * (feval(func, a) + feval(func, b)) / 2;
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while ((e > toler) && (j < n)) || (j < 4)
j = j + 1;
hr = hr / 2;
sum = 0;
for p = 1:m
w = a + hr * (2 * p - 1);
sum= sum + feval(func, x);
end
R(j + 1, 1) = R(j, 1) / 2 + hr * sum;
mr = 2 * mr;
for k = 1:j
R(j + 1, k + 1) = R(j + 1, k) + (R(j + 1, k) - R(j, k)) / (4^k - 1);
end
e = abs(R(j, j) - R(j + 1, k + 1));
end
quad = R(j + 1, j + 1);
end
% Comments added for better code readability and understanding:
% Function: romberg_integration
% Inputs:
% - func: the function to integrate
% - a: lower integration limit
% - b: upper integration limit
% - n: maximum number of iterations
% - toler: tolerance for convergence
% Outputs:
% - R: matrix containing the Romberg integration table
% - quad: final estimate of the integral
% - e: error estimate of the integral
% - hr: step size
% The function implements Romberg's method for numerical integration.
% Romberg's method improves upon the trapezoidal rule by successively
% refining the estimate of the integral using Richardson extrapolation.
% It is an iterative process that doubles the number of function evaluations
% in each iteration until the desired tolerance is reached or the maximum
% number of iterations is reached.
MATLAB Release Compatibility
Created with
R2023a
Compatible with any release
Platform Compatibility
Windows macOS LinuxTags
Acknowledgements
Inspired by: Romberg
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