Error plot is starting at the wrong value in my "while loop"

clear all
w=(12.35)^0.5;
%theta_exact=10*exp(-2*t)*cos(t*w)+20*exp(-2*t)*sin(w*t);
theta1(1)=10; %deg
psy1(1)=0; %deg/s
g=9.81; %m/s^2
c=4; %1/s
l=0.6; %m
dt1=0.1;
t1(1)=0;
i=1;
while t1<6  
    theta1(i+1)=theta1(i)+psy1(i)*dt1
    psy1(i+1)=(-g/l)*dt1*theta1(i)+(1-c*dt1)*psy1(i);
    theta_exact=10.*exp(-2.*t1).*cos(w.*t1)+(20/w).*exp(-2.*t1).*sin(w.*t1)
    epsilon1=(theta1(i)-theta_exact)
    t1(i+1)=t1(i)+dt1;
    i=i+1;
    
end
figure(1); clf;
hold on
plot(t1,theta1,'red')
plot(t1(1:end-1),theta_exact,'blue')
figure(2); clf;
plot(t1(1:end-1),(epsilon1))

If you read the code you notice that the second plot is a time vs "epsilon1". My issue is that the first value for "epsilon1" is -10 but epsilon1=(theta1(i)-theta_exact), where theta1(i) and theta_exact are the same value for their first values. The first value should read 0 for epsilon1, can anyone help me figure out why this is not the case?

Answer 1

[VBBV]

while t1<6  
    theta1(i+1)=theta1(i)+psy1(i)*dt1
    psy1(i+1)=(-g/l)*dt1*theta1(i)+(1-c*dt1)*psy1(i);
    theta_exact(i)=10*exp(-2*t1(i))*cos(w*t1(i))+(20/w)*exp(-2*t1(i))*sin(w*t1(i))
    epsilon1(i)=(theta1(i)-theta_exact(i))
    t1(i+1)=t1(i)+dt1;
    i=i+1;    
end

As you are using while loop use the counter, i for epsilon1 and theta_exact