Romberg integration method with Matlab

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Fausto Pachecco Martínez 2021-11-28

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https://ww2.mathworks.cn/matlabcentral/answers/1597459-romberg-integration-method-with-matlab

评论： Nidia 2023-11-20

I have the following code that uses the Romberg method to give the result of a definite integral, but I only want it to display the last result and not all the values of the table, how can I do this using another function to call Romberg's function?

function romberg_value = IntegrationRomberg (expression, a, b, m)
% This function evaluates an integral by the Romberg method
% Receives as parameter the variables expression, a, b, m
% Expression => function to evacuate
% a = lower limit of the interval
% b = upper limit of the interval
% m = number of subintervals
% Convert expression to a function
 f = inline (expression);
 
 h = b-a;
 r = zeros (2, m + 1);
 r (1,1) = (f (a) + f (b)) / 2 * h;
 fprintf('\nRomberg integration table:\n')
 fprintf ('\n %7.2f \n\n', r (1,1));
 for i = 2: m
    romberg_value = 0;
    for k = 1: 2 ^ (i-2)
       romberg_value = romberg_value + f (a + (k-0.5) * h);
    end
    r(2,1) = (r(1,1) + h * romberg_value) / 2;
  
    for j = 2: i % Apparently this "for" displays the other values of the table, if you comment it, 
       l = 2 ^ (2 * (j-1)); % only the first column of values appears and the others are only zeros.
       r (2, j) = r (2, j-1) + (r (2, j-1) -r (1, j-1)) / (l-1);
    end
    for k = 1: i
       fprintf ('% 7.5f', r (2, k));
    end
 
    fprintf ('\n\n');
    h = h / 2;
    for j = 1: i
       r (1, j) = r (2, j);
    end
 end

Here is the program where you can call the code above introducing the values of your variables:

% This program asks the user for the data necessary for a numerical integration
 
%Clear all
clc %Clean command window
clear all   %Clears or removes variables from main memory
close all   %Close all graphics windows
%Ask the user for the expression of the function
expression = input ('Enter the expression of the function:', 's'); %Read from keyboard converting to string
%Ask the user for the values of a, b and m
a = input ('Enter the value of the lower limit a: ');
b = input ('Enter the value of the upper limit b: ');
m = input ('Enter the number of intervals m: ');
%Calculate the integral
disp ('%%%%%% Romberg method %%%%%%%%%%')
integralValue = IntegrationRomberg (expression, a, b, m);
%Show result on screen
fprintf ('\n The integral of %s evaluated from %7.2f to %7.2f is: %7.5f \n\n', expression, a, b, integeralValue')