{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lec10_derivatives2 - Computing derivatives of functions...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Computing derivatives of functions Forward & Backward Difference Higher order derivatives Derivatives on a mesh Richardson extrapolation to improve accuracy HW#4 due Thurs –make sure to get addendum (#3) on web. You should be reading in Appendix A.1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Cost: Here error is of order h (not h 2 ), so approximation is not as good. Benefit: self starting (don’t need values before AND after the point at which you are interested). f ( x 0 ) = f ( x 0 + h ) f ( x 0 ) h O ( h ) f ( x 0 ) = f ( x 0 ) f ( x 0 h ) h + O ( h ) Forward Difference Approximation Backward Difference Approximation
Background image of page 2
Second derivative is a derivative of the derivative of a function. It is a measure of the CURVATURE (rate of change of the rate of change) of the function at that point. Second order derivatives can be found by ADDING the two Taylor expansions and rearranging for f’’(x) : f ( x 0 ) f ( x 0 h ) 2 f ( x 0 ) + f ( x 0 + h ) h 2 + O ( h 2 )
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Theory suggests that the smaller h is, the better the approximation.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}