SKEDSOFT

This method is used to derive derivative of a numerical function f(x) using newton's forward difference formula.

Derivatives Using Newton’s Forward Difference Formula :

Consider the data (x_i, f(x_i)) given at equispaced points x_i = x₀ ih, i = 0, 1, 2, ..., n where h is the step length. The Newton’s forward difference formula is given by

....................1.1

Set x = x₀ sh. Now, (1.1) becomes

.....................1.2

Note that,

The magnitudes of the successive terms on the right hand side become smaller and smaller.

Differentiating (1.2) with respect to x, we get

....................1.3

At x = x₀, that is, at s = 0, we obtain the approximation to the derivative f ′(x) as

............................1.4

Differentiating (1.3) with respect to x, we get

......................1.5