why is my ea not being recognized?

Prashant Kumar answered . 2024-12-21 00:46:55

clc; clearvars;
L = 1.25; E = 50000; I = 30000; w0 = 2.5;
syms f(x)
f(x) = (w0/(120*E*I*L))*(-x^5+2*(L^2)*(x^3)-(L^4)*x);
df = diff(f,x); 
true = double(df(2)); 
roots = vpasolve(f==0, x);
true_roots =double(roots(:));
xl = 200;
xu = 300;
xr = (xl + xu) / 2;
es = 0.001;
xr_new(1) = xr;
if double(f(xl)) * double(f(xu)) >0
    disp('The function changes sign within this bound')
    for i = 1:100
        val(i) = double(f(xl)) * double(f(xr_new(i)));
        if val(i) < 0
            disp('The root lies in the lower interval')
            xu = xr_new(i);
        elseif val(i) > 0
            disp('The root lies in the upper interval')
            xl = xr_new(i);
        else val == 0;
            fprintf('The approximate root of the function is %1.2f \n',xr_new(i))
            break
        end
        xr_new(i+1) = (xl + xu) / 2;
        ea = abs((xr_new(i+1) - xr_new(i))./xr_new(i+1));
        if ea < es
            break
        end
    end
else
    disp('The function does not change sign within this bound')
end

The function changes sign within this bound
The root lies in the upper interval
The root lies in the upper interval
The root lies in the upper interval
The root lies in the upper interval
The root lies in the upper interval
The root lies in the upper interval
The root lies in the upper interval
The root lies in the upper interval

% Print the results
ea = ea*100;
fprintf('The absolute approximate error is: %1.5f \n',ea)

The absolute approximate error is: 0.06515 

n_iterations = i+1;
fprintf('The total number of iterations are: %d \n',n_iterations)

The total number of iterations are: 9 

root = xr_new(1,end);
fprintf('The approximate root of the function is: %1.5f \n', root)

The approximate root of the function is: 299.80469 

x1 = -1000 : 1000;
y1 = double(f(x1));
xmin = -1000; xmax = 1000; ymin = -0.5; ymax = 0.5;
figure(1)
plot(x1, y1)
hold on
plot(true_roots,0,'mo','MarkerFaceColor','m')
set(gca,'XAxisLocation','origin','YAxisLocation','origin','XMinorTick','on')
xlabel('x \rightarrow')
ylabel('\uparrow f(x)')
title('Graphical root')
hold off

figure(2)
Fun = @(x) (w0/(120*E*I*L))*(-x.^5+2*(L^2)*(x.^3)-(L^4)*x);
fplot(Fun, [-1.5, 1.5], 'kx-')
hold on
plot(true_roots,0,'mo','MarkerFaceColor','m')
set(gca,'XAxisLocation','origin','YAxisLocation','origin','XMinorTick','on')
xlabel('x \rightarrow')
ylabel('\uparrow f(x)')
title('Graphical root')

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