Lecture 23 Numerical Differentiation p p CISE 301_Topic 6 First order derivatives High order derivatives Richardson Extrapolation Examples KFUPM 2
Motivation How do you evaluate the derivative of a tabulated function. p How do we determine the velocity and acceleration from tabulated measurements. p CISE 301_Topic 6 KFUPM Time (second) Displacement (meters) 0 30. 1 5 48. 2 10 50. 0 15 40. 2 3
Recall CISE 301_Topic 6 KFUPM 4
Three Formulas CISE 301_Topic 6 KFUPM 5
The Three Formulas + CISE 301_Topic 6 KFUPM 6
Forward/Backward Difference Formula CISE 301_Topic 6 KFUPM 7
Central Difference Formula CISE 301_Topic 6 KFUPM 8
The Three Formulas (Revisited) CISE 301_Topic 6 KFUPM 9
Higher Order Formulas CISE 301_Topic 6 KFUPM 10
Other Higher Order Formulas CISE 301_Topic 6 KFUPM 11
Example Richardson Table CISE 301_Topic 6 KFUPM 18
Example Richardson Table 1. 08483 1. 08988 1. 09156 1. 09115 1. 09157 This is the best estimate of the derivative of the function. All entries of the Richardson table are estimates of the derivative of the function. The first column are estimates using the central difference formula with different h. CISE 301_Topic 6 KFUPM 19