Help with Numerical Differentiation

Numerical Differentiation is pretty new to me i want to set the program to plot 2 graphs using first order forward,when i change the x=0:40:520 to x=0:20:520 i get the error index exceeds the number of array elements(26) how do i fix this error?

clear; 
clc;
x=0:40:520;
F=[0 139 298 433 685 1026 1279 1373 1490 1634 1800 1986 2417 2651 2915 3303 3516 3860 4216 4630 5092 5612 6184 6760 7327 7581];
h=x(2)-x(1) ;
n=length(x) ;
xForward=x(1:n-1);
dFForward=(F(2:n)-F(1:n-1))/h;
xBackward=x(2:end);
dFBackward=(F(2:n)-F(1:n-1))/h;
xCenteral=x (2:n-1);
dFCentral=(F(3:n)-F(1:n-2))/(2*h);


hold on
plot (xCenteral,dFCentral,'r' )
plot (xForward,dFForward, 'k')
plot (xBackward,dFBackward,'g')
legend ('centeral','Forward','Backward')
title('NUMERICAL DIFFERENCING USING STEP SIZE 40s')
xlabel ('Time')
ylabel ('Acceleration')

[Clayton Gotberg]

Do you have a more specific programming question? I'm happy to help with logical trouble or understanding a function but I don't want just to give you code that you could turn in for an assignment.

[jacob booth]

i have edited the question i can figure out how to get rid of this error

Answer 1

[Clayton Gotberg]

The error is because you have increased the number of elements in the time array x too high for the number of elements in the result array F. When you asked for x = 0:40:520 you got 14 elements to match the first 14 elements in F - note that F(14) is not the last F - but when you used x = 0:20:520 you got 27 time elements with only 26 result elements.

I think this raises two problems for you.

First, do you need to increase the number of results or decrease your time interval? For example, is it meant to stop at t = 500 instead?

Second, you're supposed to span the whole interval even with h = 40, so you need to find a way to make the number of results equal to the number of times. For example, you could pull out every other sample until you reach the end:

h = 20;
x = 0:h:520; %1x14
F = [0 139 298 433 685 1026 1279 1373 1490 1634 1800 1986 2417 2651 ...
    2915 3303 3516 3860 4216 4630 5092 5612 6184 6760 7327 7581]; %1x26
% Ellipses let you separate lines for readability
n = length(x);
sampling_rate = ceil(40/h); % Here, 20 is 1/2 of 40 so you want every other sample.
% Note that this only works well when h is 1/n of 40 (n is an integer) because
% otherwise you're not skipping whole numbers.
F_sampled = F(1:sampling_rate:end); % Get every other value in F

plot(x,F_sampled)
% This code still won't work with the F vector provided here because it's
% one value short from what it expects. F_sampled is 1x13 but x is still
% 1x14.

[Clayton Gotberg]

Apologies for the earlier code - I wrote it on mobile and it showed.