Newton's Method Convergence Plot

Im currently trying to creat a convergence plot for my Newton's Method code. But I keep on getting a function error message that says Index exceeds the numbers of elements. I'm not really sure how to fix it.

function x_root = newtonze(x_est, tol, max_iter)

w = 20*10^3; L = 4; E = 70*10^9; I = 52.9*10^(-6);

for i = 1:max_iter

Xi = x_est - ((w*(7*L^4 - 30*L^2*x_est^2 + 15*x_est^4))/(360*E*I*L))/(-(w*x_est*(L^2 - x_est^2))/(6*E*I*L));

if abs((Xi-x_est)/x_est) < tol

x_root = Xi;

break

end

x_est=Xi;

end

x_root=x_est;

hold on

% Plot evolution of the solution

figure('Color','White')

plot(0:max_iter-1,x_root(1:max_iter),'o-')

title('Newton''s Method Solution: $f(x) = x + x^{\frac{4}{3}}$','FontSize',20,'Interpreter','latex')

xlabel('Iteration','FontSize',16)

ylabel('$x$','FontSize',16,'Interpreter','latex')

end

Answer 1

[Sid Singh]

Hi, you are trying to plot a scalar value "x_root" against a time series which is why you are getting the error. Create an array

x_root = zeros(1, max_iter);
for i = 1:max_iter
    Xi = x_est - ((w*(7*L^4 - 30*L^2*x_est^2 + 15*x_est^4))/(360*E*I*L))/(-(w*x_est*(L^2 - x_est^2))/(6*E*I*L));
    if abs((Xi-x_est)/x_est) < tol
        x_root(i) = Xi;
        break
    end
    x_est=Xi;
end

and store values in that array. You would get zeros in the plot where this

if abs((Xi-x_est)/x_est) < tol

condition is not being met.