Chapter 4  Numerical Differentiation and Integration

 

Instability of Numerical Differentiation by Finite Approximation

 

   Approximating  

1.   Forward difference

.

2.   Central difference3 points

.

3.   Central difference5 points

.

 

 

   Approximating

1.   Central difference3 points

.

2.   Central difference5 points

.

   All numerical differentiation methods by finite difference approximation are unstable due to the growth of roundoff error as .

 

References:

【1】             R. L. Burden and J. D. Faires, Numerical Analysis, PWS, Boston, 1993.