Blank figures appearing for plots

I've create an adaptive time-stepping function and I'm trying to plot the graphs but it is just creating blank figures.

Here is my function:

function [tvec,yvec,dtvec]=adaptive_euler(f,ytrue,y0,t0,dt0,dtmin,dtmax,tmax,alpha,beta,gamma,TOL)
    y=zeros(10^5,1);
    y(1)=y0;
    dt=zeros(10^5,1);
    t=zeros(10^5,1);
    dt(1)=dt0;
    yt=y0;
    yt1=y0;
    t(1)=t0;
    n=1;
    while (t(n)<tmax && dt(n)<dtmax && dt(n)>dtmin)
        yt=yt+dt(n)*f(t(n),yt);
        yt1=yt1+(dt(n)/2)*f(t(n),yt1);
        yt2=yt1+(dt(n)/2)*f(t(n),yt1);
        Et2=(yt2-yt)/(dt(n));
        c=TOL/norm(Et2);
        if norm(Et2) < TOL
            y(n)=yt2;
            t(n+1)=t(n)+dt(n);
            n=n+1;
        end
        dt(n) = min(max(alpha*c*dt(n-1),gamma*dt(n-1)),beta*dt(n-1));
    end
    tvec=zeros(n,1);
    yvec=zeros(n,1);
    dtvec=zeros(n,1);
    for i=1:n
    tvec(i)=t(i);
    yvec(i)=y(i);
    dtvec(i)=dt(i);
    end

yreal=zeros(n,1);
error=zeros(n,1);
for i=1:n
    yreal(i)=ytrue(tvec(i));
    error(i)=abs(yvec(i)-yreal(i));
end   
T1=table(n,error(n));

figure(1)
plot(tvec,yvec,'.',tvec,yreal,'--');
legend('Approx:','True:');
title('Graph of the Adaptive Eulers Method approximation of dy/dx=-exp(2*t)*y^2 against real values');
figure(2)
plot(tvec,dtvec)
title('Graph of the change in dt over t');
end

And here is the script:

f=@(t,y)-exp(2*t)*y^2;
t0=0;
y0=2;
dt0=0001;
dtmin=10^-10;
dtmax=0.5;
tmax=10;
alpha=0.84;
beta=4;
gamma=0.1;
TOL=0.1;
ytrue=@(t)2*exp(-2*t);
[tvec,yvec,dtvec]=adaptive_euler(f,ytrue,y0,t0,dt0,dtmin,dtmax,tmax,alpha,beta,gamma,TOL)

Thank you!

[Adam]

Simplest option - stick a breakpoint on the plotting line and look at what is in tvec and yvec or dtvec or whichever plot is causing the problem. It may be obvious then what the problem is.

As an aside, don't use a for loop like this:

tvec=zeros(n,1);
yvec=zeros(n,1);
dtvec=zeros(n,1);
    
for i=1:n
    tvec(i)=t(i);
    yvec(i)=y(i);
    dtvec(i)=dt(i);
end

It is a much slower and more convoluted version of simply

tvec = t;
yvec = y;
dtvec = dt;

And then once you've simplified it to that one would have to ask why do it at all? Why not just use t, y and dt instead of the new vectors that are an exact copy?

[Phoebe Tyson]

Because I set up the original vectors as very large vectors of zeros as I wouldn't know how many entries would be filled, but when I plot, I don't want the zeros, i just want the entries that are filled.

[Adam]

But you set them up as vectors of length n and then you copy from 1 to n from another vector into these.

[Phoebe Tyson]

Because in the original vectors, they are much longer and everything after n is a zero, n is the number of iterations my while loop runs for, while the length of the original vectors is much larger

Answer 1

[Image Analyst]

You never enter the while loop

while (t(n)<tmax && dt(n)<dtmax && dt(n)>dtmin)

because dt(1) is 1 and dtmax is 0.5. Pass in a different dtmax.

[Phoebe Tyson]

Ah, it was supposed to be 0.001 instead of 1. now there seems to be an issue with

 dt(n) = min(max(alpha*c*dt(n-1),gamma*dt(n-1)),beta*dt(n-1));

Saying "Array indices must be positive integers or logical values."

[Image Analyst]

1 is also not less than 0.001, so that won't enter the loop either. So what did you pass in?

In the meantime, see the FAQ: Subscript_indices_must_either_be_real_positive_integers_or_logicals.