
Finite Differences
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^3
If elevation is given by 'z' and horizontal distance by 'x', use your result to calculate d^2z / 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
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...