MATLAB: How to plot multiple functions with a for loop

euler's methodfor loop

Hello, I am trying to use a for loop to solve an ODE by way of Euler's method. I have a loop that works for a single step size h = 0.05, but I was wondering if I can get the loop to run with h = [0.05 0.1 0.2], and then plot the three different outputs? Here is the code that I have so far, loops confuse me so any help is greatly appreciated.
y0 = 0;
t0 = 0;
tf = 1;
h = 0.05;
f = @(t,y) y^2 + 1;
y = y0;
y_1 = y;
for t = t0:h:tf-h
    yp = f(t,y);
    y = y + h*yp;
    y_1 = [y_1 ; y];
end
x = 0:h:1;
plot(x,y_1)

Best Answer

H =  [0.05  0.1  0.2];
figure;
hold on
for i=1:numel(H)
    y0 = 0;
    t0 = 0;
    tf = 1;
    h = H(i);
    f = @(t,y) y^2 + 1;
    y = y0;
    y_1 = y;
    for t = t0:h:tf-h
        yp = f(t,y);
        y = y + h*yp;
        y_1 = [y_1 ; y];
    end
    x = 0:h:1;
    plot(x,y_1, 'DisplayName', ['H = ' num2str(H(i))])
end
legend
Related Question