Given the elevations of five points that are equally spaced by distance 'h' in a horizontal direction, derive a general expression to determine the second derivative of slope at the central point with an accuracy of order h(adsbygoogle = window.adsbygoogle || []).push({}); ^{3}

If elevation is given by 'z' and horizontal distance by 'x', use your result to calculate d^{2}z / dx^{2}at x=10

x | 0 | 5 | 10 | 15 | 20

z | 6 | 7 | 9 | 10 | 9

I am stumped at this question with no idea where to start mainly cos its asking for the second instead of the first derivative which would just mean f_{i}= (-f_{i-1}+ f_{i+1}) / (-x_{i-1}+ x_{i+1})

Also the fact that its accuracy of order h^{3}rather than h^{2}or h^{4}etc...

Help? I'm thinking a matrix will be involved in this...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finite Differences

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**