how to solve Index exceeds the number of array elements (1).

Im writing a code base on ADAM BASFORTH 2 order to resolved a heat trasnfer problem with boundaries and I got the error message typed in the title... can someone help me out please.

There is the code...(line 27)

close all;
clc;
clear;
a=0.02;
ta=20;
dt=4;
n=5;


% initial condition
u_analytical(1)=0;
u_numerical(1)=0;
f(1)= -(a*ta) * u_numerical(1)

% for the first step, let's use analytical solution
i=2;
t(i)=(i-1)*dt;
u_analytical(i)= 7.1842 * exp(0.14*(i)) + 2.81578 * exp(0.14*(i));
u_numerical(i)=u_analytical(i);
f(1)= -(a*ta) * u_numerical(1);

% the main loop
for i=3:n
    t(i)=(i-1)*dt;
    u_analytical(i)= 7.1842 * exp(0.14*(i)) + 2.81578 * exp(0.14*(i));

    ff=1.5*f(i-1)-0.5*f(i-2);
    u_numerical(i)=u_numerical(i-1) + ff * dt;
    f(1)= -(a*ta) * u_numerical(1);    
    
    plot(t,u_analytical,'r-',t,u_numerical,'b+')
    axis([0 60 0 60 ])
    pause(0.05);
end

Answer 1

[Adam Danz]

'f' has a single value (0). In the for-loop you attempt the get the 2nd value here:

 % i = 3
ff=1.5*f(i-1)-0.5*f(i-2);
%        ^^^.....(3-2=1)

'f' will never be a vector given your current code and it will always have just 1 value so you can't index it.

Answer 2

[Fabio Freschi]

When i = 2 and inside the loop you have

f(1)= -(a*ta) * u_numerical(1);

I guess it should be

f(i)= -(a*ta) * u_numerical(1);

or

f(i)= -(a*ta) * u_numerical(i);

[Adam Danz]

or maybe

f= -(a*ta) * u_numerical;