How to avoid the warnings on my code

Hello. I have the following code and i get a few warnings. How do i fix this problem ? (I used this warning('off','all')

warning but i think it's cheating and i do not prefer it)

%--- Solving the diff. eqn. y'(t) = y(t) - c*y^2(t) with c = 0.5 using
%--- Euler's method, Runge - Kutta method, and predictor-corrector method, and comparing in graph. I have four
%--- initial values for N0

clc, clear all, close all

tmax = 100;
t = [0:tmax];
N0 = [0.1 0.5 1.0 2.0];
f = @(t,N) N - 0.5*N.^2;
h = 0.1;
L = length(t)-1;
N = zeros(1,L);

%--- Euler's method ---

for i = 1:length(N0)
    for j = 1:L
        N(1) = N0(i);
        N(1,j+1) = N(j) + h*f(':',N(j));
    end
    ylim([0 2.5])
    subplot(1,3,1), plot(t,N), str = {'Euler''s method','for the following initial conditions'}; text(40,0.5,str); hold on
    title('N'' = N - cN^2, c = 0.5')
    xlabel('t'), ylabel('N(t)')
    legend('y_0 = 0.1','y_0 = 0.5','y_0 = 1.0','y_0 = 2.0','Location','Best')
end

Warning: Ignoring extra legend entries.

Warning: Ignoring extra legend entries.

Warning: Ignoring extra legend entries.

%--- Runge - Kutta method ---

for i = 1:length(N0)
    N(1) = N0(i);
    for j = 1:tmax
        
        K1 = f(t(j),N(j));
        K2 = f(t(j) + h*0.5, N(j) + h*K1*0.5);
        K3 = f(t(j) + h*0.5, N(j) + h*K2*0.5);
        K4 = f(t(j) + h, N(j) + h*K3);
    
        N(j+1) = N(j) + h*((K1 + K4)/6 + (K2 + K3)/3);
    end
    ylim([0 2.5])
    subplot(1,3,2), plot(t,N), str = {'Runge - Kutta method','for the following initial conditions'}; text(40,0.5,str); hold on
    title('N'' = N - cN^2, c = 0.5')
    xlabel('t'), ylabel('N(t)')
    legend('y_0 = 0.1','y_0 = 0.5','y_0 = 1.0','y_0 = 2.0','Location','Best')
end

Warning: Ignoring extra legend entries.

Warning: Ignoring extra legend entries.

Warning: Ignoring extra legend entries.

[John D'Errico]

Lol. You can call it cheating to turn the warnings off. But I'd just call it dangerous in a sense, in that warnings were put there for a reason, to tell you that something bad is probably happening, and you should fix the problem.

Do you really want to turn off the warning light on your car that tells you it is overheating? Or just close your eyes to those warning signs about the bridge being out? ;-) I think you are right. Better to fix the problem.

Answer 1

[Torsten]

%--- Solving the diff. eqn. y'(t) = y(t) - c*y^2(t) with c = 0.5 using
%--- Euler's method, Runge - Kutta method, and predictor-corrector method, and comparing in graph. I have four
%--- initial values for N0
clc, clear all, close all
tmax = 100;
t = [0:tmax];
N0 = [0.1 0.5 1.0 2.0];
f = @(t,N) N - 0.5*N.^2;
h = 0.1;
L = length(t)-1;
N = zeros(1,L);
%--- Euler's method ---
for i = 1:length(N0)
    for j = 1:L
        N(1) = N0(i);
        N(1,j+1) = N(j) + h*f(':',N(j));
    end    
    subplot(1,3,1), plot(t,N),  hold on    
end
str = {'Euler''s method','for the following initial conditions'}; text(40,0.5,str);
ylim([0 2.5])
title('N'' = N - cN^2, c = 0.5')
xlabel('t'), ylabel('N(t)')
legend({'y_0 = 0.1','y_0 = 0.5','y_0 = 1.0','y_0 = 2.0'},'Location','Best')
%--- Runge - Kutta method ---
for i = 1:length(N0)
    N(1) = N0(i);
    for j = 1:tmax        
        K1 = f(t(j),N(j));
        K2 = f(t(j) + h*0.5, N(j) + h*K1*0.5);
        K3 = f(t(j) + h*0.5, N(j) + h*K2*0.5);
        K4 = f(t(j) + h, N(j) + h*K3);    
        N(j+1) = N(j) + h*((K1 + K4)/6 + (K2 + K3)/3);
    end
    subplot(1,3,2), plot(t,N),  hold on   
end
str = {'Runge - Kutta method','for the following initial conditions'}; text(40,0.5,str);
ylim([0 2.5])
legend({'y_0 = 0.1','y_0 = 0.5','y_0 = 1.0','y_0 = 2.0'},'Location','Best')
title('N'' = N - cN^2, c = 0.5')
xlabel('t'), ylabel('N(t)')

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