Asked by Bailey Smith
on 14 Jun 2018 at 22:52

Could someone please explain how to use the differences, especially with vectors? I would like to make a chart of the values of the four differences types, along with the corresponding x value. Say x=[0:0.2:0.6], y=sin(x), and yperfect=cos(x), how would I go about this?

UPDATE: This is the code I have to take the forward difference (first order).

function [out] = forwarddiff(x,y) n=1; L=length(x); while n < L out(n,1)=x(n); out(n,2)=(y(n+1)-y(n))/(x(n+1)-x(n)); n=n+1; end out(L,1)=x(L); out(L,2)=NaN; end

X and Y values can be input by the user. My new question is: Would the second order forward difference look something like this?

function [out] = forwarddiff(x,y) n=1; L=length(x); while n < L out(n,1)=x(n); out(n,2)=(y(n+2)-2*y(n+1)+y(n))/(x(n+1)-x(n))^2; n=n+1; end out(L,1)=x(L); out(L,2)=NaN; end

I get an error about exceeding matrix dimensions when I run this.

Answer by Ankita Bansal
on 18 Jun 2018 at 6:14

Accepted Answer

Hi, in line

out(n,2)=(y(n+2)-2*y(n+1)+y(n))/(x(n+1)-x(n))^2;

you are getting error because you are trying to access y(n+2) at n=L-1.

Change your code to

function [out] = forwarddiff(x,y) n=1; L=length(x); while n < L-1 out(n,1)=x(n); out(n,2)=(y(n+2)-2*y(n+1)+y(n))/(x(n+1)-x(n))^2; n=n+1; end out(L-1,1)=x(L-1); out(L-1,2)=NaN; end

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Answer by Jan
on 18 Jun 2018 at 7:58

Edited by Jan
on 18 Jun 2018 at 7:59

A shorter form of your 1st order forward difference:

function [out] = forwarddiff(x,y) x = x(:); % Consider row vectors y = y(:); dy = (y(2:end) - y(1:end-1)) / (x(2:end) - x(1:end-1)); out = [x, [dy; NaN]]; end

If you really want to do this with a loop, care for a pre-allocation. Letting the output grow iteratively wastes a lot of resources.

See also the `diff` command and `gradient`.

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## 3 Comments

## John D'Errico (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405770-forward-backwawrd-central-and-perfect-difference#comment_578948

Why not try something, then ask for help when you get stuck? Show what you did. Make an effort.

## Jan (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405770-forward-backwawrd-central-and-perfect-difference#comment_578979

I agree with John. Please try it, post the code and ask a specific question. It is unlikely that the forum will do your work in exactly the way you need it.

Is this your homework?

## Bailey Smith (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405770-forward-backwawrd-central-and-perfect-difference#comment_579069

An old homework, but no Matlab required. I've been wanting to take my old homeworks and code them into Matlab so that I can better understand the program before I take any advanced computing class. If I have time, I will try to get a code posted tonight or tomorrow.

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