SKEDSOFT

Relations between differences and derivatives:

We write Ef(x) as

where,

Hence, we obtain the operator relation,

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

In terms of the forward, backward and central differences, we obtain

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

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

Also,

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

Hence,

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

Using the Taylor series expansions, we get

Neglecting the higher order terms, we get the approximation,

.............................1.6

The error term is given by,

Hence, we call the approximation given in (1.6) as a first order approximation or of order  O(h).