1. Numerical Differentiation Chapter 23
Notion of numerical differentiation has been introduced in Chapter 4. In this chapter more accurate formulas that retain more terms will be developed.
by Lale Yurttas, Texas A&M University
Chapter 23

2. High Accuracy Differentiation Formulas
High-accuracy divided-difference formulas can be generated by including additional terms from the Taylor series expansion.

3. Inclusion of the 2nd derivative term has improved the accuracy to O(h2).
Similar improved versions can be developed for the backward and centered formulas as well as for the approximations of the higher derivatives.
by Lale Yurttas, Texas A&M University
Chapter 23