Using Finite Difference Method In Excel

[elliottmarter]

------Question------​

a) Research the three finite difference approximations mentioned above (forward, backward and central). Use a spreadsheet to demonstrate each of these numerical methods for the function below.

y=x³ −x² +0.5x​

Investigate the derivative over the range x = [0,1], using finite differences of 0.1

b)Plot the results from each method onto one graph, along with the analytical derivative of the function. Make sure your plot includes a legend.

------Answer------​

i can see that this is a really (really) easy question if you know how to utilise the finite differences method in excel, however as you can see from the question were weren't taught it and we have to research it, so i went to wikipedia (obviously!)

so anyway i see on wikipedia they have this:

which i can partially understand, you just insert your function where it says f(x) and then link you x values to a table of values 0-1 in 0.1 steps, but i don't understand what the "h" stands for, then for part b i guess by analytical derivative it means just standard differentiation so:

y=x³ −x² +0.5x

$$\stackrel{dy}{dx}$$=3x²-2x+0.5​

if anyone could lend a hand or a link to a good "dummies guide" web page I'd be very grateful.

Thanks
Elliott M

 

[BishopUser]

h is your step. so in your case h = .1

That is kind of intuitive when you look at the equations. For the forward difference calculation you are adding +h which gives you the "forward difference" while for the backward difference calculation you subtract h in order to get the backward difference. Of course the central difference you add and subtract half your step to be in the middle. As for part B you are correct. The point of this exercise is probably to compare the accuracy of analytical differentiation with numerical differentiation (finite difference).