second order finite difference scheme

I am given data t=[0 1 2 3 4 5] and y(t)=[1 2.7 5.8 6.6 7.5 9.9] and have to evaluate the derivative of y at each given t value using the following finite difference schemes.

(y(t+h)−y(t−h))/2h =y′(t)+O(h^2)
(−y(t+2h)+4y(t+h)−3y(t))/2h =y′(t)+O(h^2)
(y(t−2h)−4y(t−h)+3y(t))/2h =y′(t)+O(h^2)

I started the code, but I haven't learned what to do in the second order case. This what I have so far for the first given equation:

t= 0: 1: 5;
y(t)= [1 2.7 5.8 6.6 7.5 9.9];
n=length(y);
dfdx=zeros(n,1);
dfdx(t)=(y(2)-y(1))/(t(2)-t(1));
for i=2:n-1
    dfdx(1)=(y(i+1)-y(i-1))/(t(i+1)-t(i-1));
end
dfdx(n)=(y(n)-y(n-1))/(t(n)-t(n-1));

the error that returns is "Subscript indices must either be real positive integers or logicals." referencing my use of y(t). How do I fix this to make my code correct?

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Chad Greene]

There's no need for the (t) when you define y(t). Same with dfdx. Also, make sure you change dfdx(1) in the loop to dfdx(i).

t= 0: 1: 5;
y= [1 2.7 5.8 6.6 7.5 9.9];
n=length(y);
dfdx=zeros(n,1);
dfdx=(y(2)-y(1))/(t(2)-t(1));
for i=2:n-1
    dfdx(i)=(y(i+1)-y(i-1))/(t(i+1)-t(i-1));
end
dfdx(n)=(y(n)-y(n-1))/(t(n)-t(n-1));

[Chad Greene]

By the way, the gradient function gives the same results.

t= 0: 1: 5;
y= [1 2.7 5.8 6.6 7.5 9.9];
plot(t,gradient(y,t))

[Margaret Winding]

Thank you very much! I learned about the gradient function but my professor does not want us to use that for this problem.

I fixed the errors you mentioned, but it now gives me the same error "Subscript indices must either be real positive integers or logicals" but for dfdx=(y(2)-y(1))/(t(2)-t(1))

I don't understand what formatting error is occurring at this point, any ideas? Thank you so much!!

[Torsten]

dfdx(1)=(y(2)-y(1))/(t(2)-t(1))

Best wishes

Torsten.

[Chad Greene]

Ah, yes, sorry Margaret; thanks Torsten.

[Margaret Winding]

Chad and Torsten,

Thank you so much for your help! I was able to get the correct answer :)

[alburary daniel]

and how will be the code for using a 4-point first derivative?