Civil and Environmental Engineering 2219A/B Lecture Notes - Lecture 31: Numerical Differentiation, Richardson Extrapolation

• School: Western University
• Department: Civil and Environmental Engineering
• Course: Civil and Environmental Engineering 2219A/B
• Professor: Martha Dagnew

Document Summary

Today, we"re going to be looking at the methods of lower numerical differentiation. And we"re also going to be looking at schemes to improve the accuracy of lower order numerical differentiation formulas. It"s not something we calculate, but rather a consequence of the taylor series (from which these are derived). Just like integration, there"s three ways of improving accuracy of estimates: Recall: this uses two derivative estimates to compute a third, more accurate, approximation. These methods are literally the exact same as integration, so i"ll breeze over it. Richardson extrapolation can be used to combine two lower-accuracy estimates of the derivative to produce a higher accuracy estimate. Recall: previously we have seen that richardson extrapolation can be written as below where ( 1) and ( 2) are lower accuracy integral estimates at step sizes of 1 and h2, respectively, and representing the improved estimate.